# Light - Reflection and Refraction : Complete Set of Questions

This set of questions contains all the possible concepts
which could be asked in the examination

Q.1  What is light? What is the nature of light?

Light is a form of energy which helps us see things around us.  When light rays strikes any object that object reflects light back, when this reflected light is captured by our eyes the object becomes visible.

Light is an electromagnetic wave which does not require a material medium for propagation.

Q.2 What makes it possible to see objects around us?

The reflection of light by an object makes the object visible to our eyes.

Q.3 Why does it take some time to see objects in dim light when you enter the room from bright sunlight outside?

The pupil controls the amount of light entering our eye. It becomes smaller for larger intensity of light and reduces the amount of light entering the eye. When we enter a dimly lit room then the amount of light received by the eye is small and so the pupil expands and takes time before we can see the objects around.

Q.4 What is meant by diffraction of light?

When light waves encounter obstacles of very small sizes, the light waves bend around the edges of the obstacle and travel. This is known as Diffraction of Light.

Q.5 Does a light ray require any medium for propagation?

The light waves are transverse in nature so do not need any material medium for propagation.

Q.6 Define ray of light.

A ray of light is a straight line with arrow ahead showing the direction of the movement of light.

Q.7 Briefly explain the three different types of light beams.

Light travels in a straight line, and path of line shown by a line with an arrow is called Ray. A collection of rays originating from the same source travelling in the same direction is called a beam of light.

There are three types of light beam:

Parallel beam : The beam of light in which rays are parallel to each other.

Convergent beam : The beam of light in which rays emerges or appear to emerge at a point.

Divergent beam : The beam of light in which rays diverge or appear to diverge from a point.

Q.8 Write short note on luminous and non-luminous objects.

Luminous object: These are objects which emit light of their own. For example, Sun, Bulb.

Non Luminous object: These are objects which do not emit light of their own but reflect light coming from other sources.  For example, Moon.

Reflection of Light

Q.9  Define Reflection.

The bouncing back of rays of light from a polished and shiny surface is called reflection or reflection of light. It is similar to bouncing back of a football after colliding with a wall or any hard surface.

Q.10 State the laws of reflection :

Laws of Reflection of light :

The two laws of reflection are :

• The incident rays, reflected rays and normal at the point of incidence, all the three lies on the same plane.

• In every case, the angle of incidence is equal to the angle of reflection.

∠i = ∠ r

This law is applicable for all type of mirrors, plane mirrors as well as spherical mirrors.

Q.11 Write one difference and one similarity between Regular and Diffuse Reflection.

Difference

Regular Reflection : The reflection of light through a smooth or polished surface.

The parallel light rays falling on the surface get reflected such that the refracted rays are parallel to each other.

Diffuse or irregular Reflection : The reflection of light through a rough surface.

The parallel light rays falling on the surface get reflected such that the refracted rays are in different directions and no definite image is formed but the surface becomes visible.

Similarity

Both in Regular or irregular Reflection the angle of reflection and angle of incidence are same.

Q.12 What is a plane mirror?

A mirror is a reflective surface that does not allow the passage of light and instead bounces it off, thus producing an image. The most common mirrors are flat and called plane mirrors. These mirrors are made by putting a thin layer of silver nitrate or aluminium behind a flat piece of glass.

For light rays striking a plane mirror, the angle of reflection equals the angle of incidence.

Q.13 State the characteristics of the image formed by a plane mirror

Formation of image in plane mirror:

1. A plane mirror always forms virtual and erect image.

2. The distance of image and that of object is equal from the mirror.

3. The image formed by a plane mirror is laterally inverted.

4. The size of the image is equal to the size of the object.

Q.14 Name the metal which is the best reflector of light.

Silver is the metal which acts as a best reflector for light rays.

Q.15  What are mirrors? Define its type.

A highly polished surface capable of reflecting almost all the light falling on it is known as mirror. The different types of mirror are:

1. Plane mirror: Type of mirror with plane surface and image formed is laterally inverted, erect, virtual and of the same size as that of object.

2. Spherical mirror: It is a part of hollow sphere with one surface silvered so that it becomes smooth and reflects light regularly means a large fraction of the incident light is reflected back along a definite direction.

Q.16 What is a curved mirror?

A curved mirror is a mirror with a curved reflective surface. Basically these curved surfaces are parts of spherical surfaces and hence they are also called as spherical mirrors. Curved mirrors have extensive uses in various applications.

Q.17 What is lateral inversion? Explain by giving suitable example:

If an object is placed in front of a mirror, then the right side of the object appears to be the left side and the left side appears to be the right side of this image. This change of sides of an object and its mirror image is called lateral inversion.

For example, the alphabet ‘F’ will look laterally inverted.

Q. 18 What happens when a line falls on a plane mirror perpendicularly?

If light rays fall perpendicularly to the surface of plane mirror, the light rays reflect back along the same path, i.e. retraces its path back.

∠i = ∠ r

Mirrors

Q.19 Define image. What are the two types of images?

When a number of rays starting from a point after suffering reflection or refraction converge to meet or appear to meet(diverge from) a second point, then this second point is called the Image of the first point.

Image formed is of two types :
1. Real image
2. Virtual image

1. Real image :
If the rays of light starting from a point after suffering reflection or refraction actually meet at the second point, then the image formed  will be real as shown in fig.1. Real image can be taken on screen.
2. Virtual image :
If the rays starting from a point after suffering reflection or refraction do
not actually meet but appear to diverge from a second point, then this type of image formed is virtual in nature. e.g., when we look our face in a plane mirror, we see an virtual image of our face in the plane mirror.

Q.20 With the help of a diagram, show arrangement of two plane mirrors, such that incident ray and reflected ray becomes parallel to each other irrespective of angle of incidence.

Incident ray and reflected ray will always be parallel to each other if two plane mirrors are placed perpendicular to each other as shown in figure.

Construct ray diagrams to illustrate the formation of a virtual image in a plane mirror

1. First you draw your object, a short straight line will do to keep things simple. And you draw a plane mirror in the centre.

2. You draw light rays as straight lines from the 2 ends of your line, 2-3 will do.

3. Reflect this off the plane mirror in the centre of your page. (Remember the law of reflection, the angle of incidence=the angle of reflection.)

4. Then you extend these reflected light rays beyond the plane mirror. Like the above diagram. See how the dotted lines are extended 'into' the mirror?

5. Remember you drew lines from both ends of your object? Well where the dotted lines meet behind the mirror will form the 2 ends of the virtual image of your object. Try it!

6. Notice that the virtual image is the same size as the object, but is laterally inverted.

7. Lateral inversion is basically reversing your image from left to right. If you look in a mirror and part your hair to your left, when people see you they actually see the hair parting as to the right.

Q.21 Mention some uses of plane mirrors:

A plane mirror is used:

• As a looking glass to view ourselves

• By interior designers to create an illusion of depth

• To fold light as in a periscope and other optical instruments

• To make kaleidoscope, an interesting toy

Spherical Mirrors

Q.22 What are the different types of spherical mirrors?

Types of Spherical Mirror :

Concave Mirror : Spherical mirror with reflecting surface curved inwards is called concave mirror. A concave mirror is also known as Converging Mirror as it converges the incident rays after reflection.

Convex Mirror : Spherical mirror with reflecting surface curved outwards is called convex mirror. A convex mirror is also known as Diverging Mirror as it diverges the incident rays after reflection.

Q.23 Define the following terms in the case of spherical mirror

1. Pole

2. Centre of curvature

4. Aperture

5. Principal axis

6. Principal focus

7. Focal length

1. Pole : The centre of reflecting surface of a spherical mirror is known as Pole. Pole lies on the surface of spherical mirror. Pole is generally represented by ‘P’. The middle point of the mirror is  called pole of the mirror.

2. Centre of Curvature : The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C.

In the case of concave mirror centre of curvature lies in front of the reflecting surface. On the other hand, centre of curvature lies behind the reflecting surface in the case of convex mirror.

Fig: Convex Mirror

3. Radius of Curvature: The radius of sphere of which the reflecting surface of a spherical mirror is a part  is called the Radius of Curvature of the spherical mirror. The radius of curvature of a spherical mirror is denoted by letter ‘R’.

Similar to centre of curvature, radius of curvature lies in front of concave mirror and lies behind the convex mirror and is not a part of the mirror as it lies outside the mirror.

4. Aperture: The diameter of reflecting surface of a spherical mirror is called aperture.

5. Principal Axis: Imaginary line passing through the centre of curvature and pole of a spherical mirror is called the Principal Axis.

6. Focus or Principal Focus: Point on principal axis at which parallel rays coming from infinity converge after reflection is called the Focus or Principal Focus of the spherical mirror. Focus is represented by letter ‘F’.

Fig: Converging Mirror

In the case of a concave mirror, parallel rays coming from infinity  converge after reflection in front of the mirror. Thus, the focus lies in front of a concave mirror.

Fig : Diverging Mirror

In the case of a convex mirror, parallel rays coming from infinity appear to be diverging from behind the mirror. Thus, the focus lies behind the convex mirror.

7. Focal length: The distance from pole to focus is called focal length. Focal length is denoted by letter ‘f’. Focal length is equal to half of the radius of curvature.

$Or,f = {R\over 2}$            Or , R = 2f

Q.24 Define “aperture” of a spherical mirror.

The diameter of the reflecting surface of spherical mirror is called its aperture.

Q.25 How many rays are required for the formation of image of the point object?

The intersection of at least two reflected rays give the position of image of the point object.

Q.26 Explain the rules for obtaining Images Formed by Spherical Mirrors Using Ray Diagrams:

The different ways in which a ray of light is reflected from a spherical mirror are :

Case I:

#### Reflection of Rays parallel to Principal Axis :

In the case of concave mirror : A Ray parallel to principal axis passes through the principal focus after reflection from a concave mirror.

Similarly, all parallel rays to the principal axis pass through the principal focus after reflection from a concave mirror. Since, a concave mirror converge the parallel rays after reflection, thus a concave mirror is also known as converging mirror.

In the case of convex mirror : A ray parallel to principal axis appears to diverge from the principal focus after reflecting from the surface of a convex mirror.

Similarly, all rays parallel to the principal axis of a convex mirror appear to diverge or coming from principal focus after reflection from a convex mirror. Since, a convex mirror diverges the parallel rays after reflection, thus it is also known as diverging mirror.

##### Case 2 Reflection of ray passing through the Principal Focus :

In the case of concave mirror: Ray passing through the principal focus goes parallel to principal axis after reflection in the case of concave mirror.

Fig : Ray passing through principal focus

In the case of convex mirror : A ray directed towards principal focus goes parallel to principal axis after reflecting from the surface of a convex mirror.

Fig : Ray through principal focus

#### Ray passing through the Centre of curvature:

A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path. The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface

Case 4

Ray incident obliquely to the principal axis: Ray obliquely to the principal axis goes obliquely after reflecting from the pole of the both concave and convex mirror and at the same angle.

A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror [Fig. (a)] or a convex mirror [Fig. (b)], is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.

In all the above cases, the laws of reflection are followed. At the point of incidence, the incident ray is reflected in such a way that the angle of reflection equals the angle of incidence.

Q.27 Draw the ray diagram for the concave mirror when:

1. The object is at infinity.

2. The object is beyond ‘C’

3. The object is at ‘C’

4. The object is between ‘C’ and ‘F’

5. The object is at ‘F’

6. The object is between ‘P’ and focus

Ray diagrams for the formation of image by a concave mirror for various positions of the object are-

1. Object at infinity :

Since parallel rays coming from the object converge at principal focus, F of a concave mirror; after reflection. Hence, when the object is at infinity the image will form at F.

Properties of image :

• Point sized

• Highly diminished

• Real and inverted

2. Object between infinity and Centre of Curvature:

When object is placed between infinity and centre of curvature of a concave mirror the image is formed between centre of curvature (C) and focus (F).

Properties of image :

• Diminished compared to object

• Real and inverted

3. Object at Centre of Curvature (C) :

When the object is placed at centre of curvature (C) of a concave mirror, a real and inverted image is formed at the same position.

Properties of image :

• Same size as object

• Real and inverted

4. Object between Centre of curvature (C) and Principal Focus (F) :

When the object is placed between centre of curvature and principal focus of concave mirror, a real image is formed beyond the centre of curvature (C).

Properties of image:

• Larger than object

• Real and inverted

5. Object at Principal Focus (F) :

When the object is placed at principal focus (F) of a concave mirror, a highly enlarged image is formed at infinity.

Properties of image:

• Highly enlarged

• Real and inverted

6. Object between Principal Focus (F) and Pole (P) :

When the object is placed between principal focus and pole of a concave mirror, an enlarged, virtual and erect image is formed behind the mirror

Properties of image:

• Enlarged

• Virtual and erect

Q.28 Illustrate through the ray diagrams the image formation by a convex mirror for different positions of the object

There are only two possibilities of position of object in the case of a convex mirror, i.e. object at infinity and object between infinity and pole of a convex mirror.

1. Object at infinity: When the object is at the infinity, a point sized image is formed at principal focus behind the convex mirror.

2. Properties of image: Image is highly diminished, virtual and erect.

3. Object between infinity and pole: When the object is between infinity and pole of a convex mirror, a diminished, virtual and erect image is formed between pole and focus behind the mirror.

Properties of image: Image is diminished, virtual and erect

Q.29 State the uses of concave mirror:

Some of the uses of concave mirror are -

• Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light.

• As shaving mirror to produce larger image of face to facilitate better viewing during shaving.

• Concave mirror is used by dentists to see larger image of teeth of the patient. When a tooth is placed between focus and pole, the concave mirror produces a magnified image of the tooth.

• As reflector in solar furnace. By using concave mirror in solar furnace the concentrated rays of sunlight is obtained at focus which produces enormous amount of heat because of concentration.

Q.30 State the uses of convex mirrors:

Some of the uses of convex mirrors are -

• Convex mirror is used in rear view mirror of vehicles; so that the driver can see the traffic coming from behind. The field of view is widest in case of a convex mirror, which enables it to show a wider area from behind.

• Convex mirror is used on hairpin bends on the road; so that the driver can see the traffic approaching from another side of the bend.

Q.31 What is meant by New Cartesian Sign Convention and write the sign conventions used for measuring distances in case of spherical surfaces

Reflection of light by spherical mirrors follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole(P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the X-axis(X’X) of the coordinate system.

The conventions  for spherical mirrors are as follows -

• The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left hand side.

• All distances parallel to the principal axis are measured from the pole of the mirror.

• All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

• Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

• Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative

Q.32 Explain the sign conventions to be followed for concave and convex mirrors :

• Since, object is always placed in front of the mirror hence the sign of object is taken as negative.

• Since, the centre of curvature and focus lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.

• When image is formed in front of the mirror, the distance of image is taken as (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).

• Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.

• Since, object is always placed in front of the mirror hence the sign of object is taken as negative.

• Since, the centre of curvature and focus lies behind the convex mirror, so sign of radius of curvature and focal length are taken as + (positive) in the case of convex mirror.

• In the case of convex mirror, image always formed behind the mirror, thus the distance of image is taken as positive.

• In the case of a convex mirror, always an erect image is formed, thus the height of image is taken as positive.

Q.33  A mirror is having focal length of -20 cm. Identify the mirror.

It’s a concave mirror.

Q.34 In a row there are placed plane mirror, convex and concave mirror, how can a person identify them by merely looking at them?

A person standing in front of a mirror and looking into it can easily identify the type of mirror he is looking in. If the image formed in the mirror is of same size and erect then the mirror would be plane mirror. If the image formed by the mirror is bigger in size and erect then the mirror would be concave mirror. If the image formed in the mirror is of smaller size and erect then the mirror would be convex mirror.

Q.35 Why convex mirrors are known as divergent mirrors whereas the concave mirrors are called convergent mirrors?

When light rays fall on a convex mirrors the reflected rays usually diverging from the point of incidence. Therefore, known as Diverging mirrors.

While in case of concave mirrors the light falling on its surface usually converges after reflection, thus known as Converging mirrors.

Q.36 Where will be an image formed when an object is placed at the focus of a concave mirror?

When an object is placed at focus of a concave mirror the image formed will be at infinity.

Q.37 Mirrors have a wide range of usage in day to day life. There are some applications where mirrors are used. Against each application write the type of mirror used.

2. Solar furnace

3. Kaleidoscope

4. Rear view mirrors

2. Solar furnace: Concave mirror

3. Kaleidoscope: Plane mirror

4. Rear view mirrors : Convex mirror

Q.38 Why are convex mirror used in rear view mirrors but in solar furnace concave mirrors are used?

Convex mirror is used in side/rear view mirror of a vehicle. Convex mirrors give a virtual, erect, and diminished image of the objects placed in front of it. Because of this, they have a wide field of view. It enables the driver to see most of the traffic behind him/her.

Concave mirrors are convergent mirrors. That is why they are used to construct solar furnaces. Concave mirrors converges the light incident on them at a single point known as principal focus. Hence, they can be used to produce a large amount of heat at that point.

Q.39 Dentist uses a type of mirror in examining patient’s teeth. Which mirror is that and what is its use in dentistry.

Dentist uses concave mirrors for examining a person’s mouth to see enlarged image of tooth to be operated. This makes the dentist work easier.

Q.40 Is there any change observed in the focal length of a mirror when immersed in water?

Focal length of a concave mirror does not depend on medium, so it remains unchanged.
If refractive index of the material of convex lens is greater than that of water, then its focal length will increase.
If refractive index of the material of convex lens is equal to that of water, then its focal length will become infinity.
If refractive index of the material of convex lens is less than that of water, then its focal length will become negative i.e it will behave like concave lens.

Q.41 In shops, there are used some mirrors to have a check on theft. Name this type of mirror.

There are big convex mirrors used in the shops to keep a check on the customers resisting the chances of theft. These mirrors are used as shop security mirrors. Since Convex Mirrors are bent towards the light source, they have a wider range of view but everything is condensed and looks smaller. Convex mirrors are mainly used for their wide ranges of view as it helps people see more than plain or concave mirrors.

Q.42 Write any four uses of plane mirror in our day to day life.

Some of the uses of plane mirrors are-

•  These mirrors are used in dressing, bathroom for seeing ourselves.

•  These are fitted at blind turns on the busy roads so that the drivers could see the image of vehicle approaching and accidents could be prevented.

•  These are used in making periscope.

Q.43 State the relation between Radius of curvature and focal length of a spherical mirror

The focal length(f) of a spherical mirror whether it is a concave or convex  mirror, is equal to half of its radius of curvature(R).

$f = {R \over 2}$

Q.44 With help of a diagram, explain the following terms:

(a)I ncident ray

(b) Reflected ray

(c) Point of incidence

(d) Normal

(e) Angle of incidence

(f) Angle of reflection

(a) Incident ray: A light ray falling on a reflecting surface.

(b) Reflected ray: A light ray being retuned in the same medium after reflection.

(c) Point of incidence: A point on the reflecting surface on which the light ray falls.

(d) Normal: An imaginary line made perpendicular at the point of incidence from where if the ray falls travels back through the same path.

(e) Angle of incidence: The angle made at the point of incidence between the line of incidence and normal.

(f) Angle of reflection: The angle made at the point of incidence between the reflected ray and normal.

Q.45 What do you mean by Mirror formula?

A formula which provides a relation between image distance(v), object distance(u), and focal length(f) of a spherical mirror is known as Mirror formula.

Mirror formula:

${1 \over v} + {1 \over u} = {1 \over f}$

Where v = distance of image from the mirror

u = distance of object from the mirror

f= focal length of the mirror.

Images formed by different mirrors

Q.46 Differentiate between Real and Virtual Image.

Q.47 What are the rays used for locating the images of an object?

Following are the rays used to draw or locate the image of an object, at least two of the following are used to locate the image.

1. A ray of light parallel to the principle axis will pass (Concave mirror) or appear to pass (convex mirror) through principle focus after reflection.

2. A ray of light passing through the principal focus emerges parallel to the principal axis after reflection from the mirror.

3. A ray of light passing through or appears to pass through the centre of curvature, retraces the same path after reflection.

4. A ray of light incident obliquely on the pole of the mirror gets reflected back making the same angle. Angle of incidence = angle of reflection

Q.48 If you want to see the full length image of a building, which mirror is preferred? Concave or Convex?

We can see a full-length image of a tall building/tree in a small convex mirror.

One such mirror is fitted in a wall of Agra Fort. In the Agra Fort, we can observe the full-length image of a distant, tall building/tomb in the wall mirror.

Q.49 In a mirror, the image of an object is always diminished wherever the object may be placed. Which type of mirror is this?

The mirror is convex mirror. They always produce virtual and upright images. The image is always smaller than the object(diminished).

Q.50 An image is formed by a concave mirror as virtual, erect and larger than the object. At what position the object must be to form such image?

Object placed between pole and focus

Nature of Image: This is the only case in which we get virtual and erect image. Image is magnified and behind the mirror.

Q.51 An object is placed at four different positions 8 cm, 15 cm, 20 cm, and 25 cm from concave mirror of focal length 10 cm. At which object distance the image produced will be:

• A diminished real image
• A magnified real image
• A magnified virtual image
• An image of the same size as the object

Given,

Focal length, f = 10 cm,

Centre of curvature, C= 2f = 20 cm

• A diminished real image is formed by a concave mirror when the object is placed beyond C.

Since, the radius of curvature for this mirror is 20 cm. Therefore, the object should be placed at 25 cm.

•  A magnified real image is formed by a concave mirror when the object is placed between the F and C.

Since, F is at 10 cm and C is at 20 cm. Therefore the value between the F and c is 15. So, object should be placed at 15 cm from the mirror.

• A magnified virtual image is formed by a concave mirror when the object is placed within the Focus,F. since, focus for this mirror is 10 cm, the object should be placed at value less than 10 cm i.e. 8 cm. So, object should be placed at a distance of 8 cm from the mirror.

•  An image of the same size as the object is formed by a concave mirror when the object is at centre of curvature, C. since, C is at 20 cm. So, object should be placed at 20 cm from the mirror.

Q. 52 Between which two points related to a concave mirror should an object be placed to obtain on a screen an image twice the size of the object?

Between centre of curvature and the principal focus

When the object is placed between centre of curvature and principal focus of concave mirror, a real image is formed beyond the centre of curvature (C).

Properties of image:

•  Larger than object

•  Real and inverted

Q.53 Write an expression showing the relation between object distance(u), image distance(v), and focal length(f).

${1 \over u} = {1 \over f} - {1 \over v}$

${1 \over f} = {1 \over u} + {1 \over v}$

Q.54 What is the minimum distance between an object and its real image in case of a concave mirror?

Zero, when object is at centre of curvature, its real image is also formed at the same point.

Q.55 (a) Define linear magnification.

(b) What information does the magnitude and sign of the magnification provides about the image.

The magnification produced by a plane mirror is +1. How is the image formed of an object seen in the mirror?

(a) It is the ratio of the height of the image to the height of the object. It is usually represented by the letter m.

$Magnification(m) = {{Height{\mkern 1mu} of{\mkern 1mu} image\left( {h'} \right)} \over {Height{\mkern 1mu} of{\mkern 1mu} object\left( h \right)}}$

Relation among magnification, distance of object and distance of image:

Magnification (m) = ${{Distance{\mkern 1mu}of{\mkern 1mu} image}\over {Distance{\mkern 1mu} of{\mkern 1mu} object}} = {\nu\over u}Thus,m{{h'}\over h} = -{\nu\over u}$

Where; m = magnification, h' = height of image, h = height of object, v = image distance and u = object distance.

(b) Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. A negative sign in the value of the magnification indicates that the image is real. A positive sign in the value of the magnification indicates that the image is virtual.

(c) Magnification produced by a mirror is given by the relation

The magnification produced by a plane mirror is +1. It shows that the image formed by the plane mirror is of the same size as that of the object. The positive sign shows that the image formed is virtual and erect.

Q.56 Identify the mirror with the nature of image formed.

(a) Image is always diminished.

(b) Image is always of equal size and equal distance as that of object.

(c) Image is always real except when object is placed between the pole and focus.

(a) Convex mirror

(b)Plane mirror

(c) Concave mirror

Q.57 Write three points about the image formation by plane mirrors.

The image formed by plane mirrors are-

•  Object Distance = Image distance

•  Object size = Image size

•  Erect

Q.58 Draw a ray diagram to show reflection of an incident ray parallel to principal axis by a convex mirror

Refraction

Q.59 Define: Opaque and Transparent substances.

1. Opaque substances: Substances through which light cannot pass. Example: wood, iron

2. Transparent substances: Substances through which light can pass. Example: air, glass, water

Q.60 Define Refraction.

Refraction is a phenomenon of bending of light when it travels from one medium to another due to differences in optical densities of the medium.

Light travels with different speed in different medium. Light travels fastest in vacuum with speed as 3 × 108 m/s.

Q.61 What is meant by optical density?

Optical density :- Medium having greater value of refractive index is called optically denser medium, this means light will travel at slower speed in optically denser medium compared to in an optically rarer medium.

Q.62 What is the cause behind refraction?

Speed of light varies with the type of medium in which it travels, lesser in denser medium and higher in the rarer one. Therefore, when light travels from a denser to rarer medium the speed of light increases and the light ray bends away from the normal rather than passing straight. On the other hand, when ray of light travels from a rarer medium to denser one it gets bend towards the normal.

Q.63 Show with the help of a diagram how a light ray passing through a rectangular glass slab gets reflected.

Light passing through the glass slab encounters refraction two times once at air to glass interface and other at glass to air interface. Following are the features:

When light (incident ray) travels from air to glass slab i.e. from rarer to denser medium it bends towards the normal making the angle of refraction ∠r  smaller than angle of incidence ∠i, ∠i > ∠r

Now this refracted ray acts as incident ray for the second interface and bends away from the normal making the angle, angle of emergence ∠e greater than the angle of refraction ∠r, ∠r < ∠e

•  If the incident ray is perpendicular to the normal or does not make any angle with the normal, then the ray passes through the glass slab straight without showing any refraction.

•  The angle of incidence will always be equal to angle of emergence. ∠i =∠e

•  The emergent ray and incident ray being extended are parallel to each other but slightly displaced laterally. This displacement of the light ray is termed as lateral displacement.

•  For the same angle of incidence, the lateral displacement would be directly proportional to the thickness of glass slab or vice-verse.

Q.64 At what angle a ray of light should strike the surface of glass, so that it does not suffer any refraction?

It should strike normally i.e., angle of incidence should be zero.

Q.65 What is Lateral Displacement?

The lateral shifting of the light ray from its original path when it travels through a glass slab due to refraction is known as lateral displacement. Perpendicular distance between the incident ray and the emergent ray is called lateral displacement.

Q.66 Point out any 4 everyday applications of Refraction of light.

(a) Bending of pencil when placed in a glass with water:

When a pencil or stick is kept in a beaker or a glass filled with water, the stick appears slightly bent. This happens because the light; entering from air (rarer medium) into water (denser medium); bends towards normal to the incident which makes the appearance of pencil or stick as bent.

(b) Position of fish in the water of pond:

The ray coming from fish in the pond bends away from the normal to the incident. We see the emergent ray which makes the appearance of fish slightly above its position.

(c) Formation of rainbow :

Rainbow is formed just after the rain. When ray of light travels from droplets of rain, it is scattered into its constituent seven colours and forms a rainbow in the sky.

(d) Visibility of sun slightly before the time of sunrise:

When the rays coming from the sun enter into atmosphere (which is denser medium than vacuum), they bend away from normal to the incidence because of refraction. Since we see the refracted rays coming from the sun, that's why the sun becomes visible slightly ahead of the time of sunrise.

Q.67 Where will you place an electric lamp from a convex lens, so that a parallel beam of light comes out of it?

The lamp should be placed at the principal focus of the lens

Q.68 Enlist the factors on which Refractive Index of a medium depends upon.

The refractive index of a medium depends on the following factors :

•  The nature of the medium

•  The color or wave length of the incident light

Q.69 How does a focal length of convex lens change if monochromatic red light is used instead of monochromatic blue light?

Because red light and blue light both have different refractive indices.

Q.70 (a) What happens to a ray of light when it travels from one medium to another having equal refractive indices?

(b)State the cause of refraction of light.

(a) It does not deviate from its path.

(b) When light travels from one medium to another medium its speed changes due to which it deviates from its path

Q.71 Write a short note on Laws of refraction of light.

When a light ray travels from one medium to another it undergoes refraction according to the two laws of refraction.

The laws of refraction of light are:

(i) The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.

(ii) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media.

This law is also known as Snell’s law of refraction. If i is the angle of incidence and r is the angle of refraction, then

${{\sin {\mkern 1mu} {\mkern 1mu} i} \over {\sin {\mkern 1mu} {\mkern 1mu} r}} = constant = {a_{\mu b}}$

where  aµ  shows that light is travelling from the medium 'a' into the medium 'b'.

i.e. aµrepresents the refractive index of medium 'b' with respect to medium 'a'.

This constant value is called the refractive index of the second medium with respect to the first

Q.72 (a) What is the refractive index and absolute refractive index of a medium?

(a) Refractive Index is the extent of change of direction of light in a given pair of media. The refractive index is a relative value of speed of light in the given pair of media.

Thus, to calculate the refractive Index the speed of light in two media is taken.

Let the speed of light in medium 1 is v1 and in medium 2 is v2

Therefore,

Refractive Index of  medium 2 with respect to medium 1

(n21) = ${{Speed\,of\,light\,in\,medium\,1}\over {Speed\,of\,light\,in\,medium\,2}}$

Above expression gives the refractive index of medium 2 with respect to medium 1. This is generally denoted by n21. to

Similarly, the refractive index of medium 1 with respect to medium 2 is denoted by n12.

Therefore,

${n_{21}}={{Speed\,of\,light\,in\,medium\,1}\over {Speed\,of\,light\,in\,medium\,2}}= {{{\upsilon _2}} \over {{\upsilon _1}}}$

Absolute Refractive Index :- When one medium is taken as vacuum and speed of light is taken in it, then the refractive index of second medium with respect to vacuum is called Absolute Refractive Index and it is generally denoted by n2.

$Thus,{n_2}= {{Speed\,of\,light\,in\,vacuum} \over {Speed\,of\,light\,in\,given\,medium\,}}$

The speed of light in vacuum is slightly faster than in air.

Let speed of light in air is 'c' and the speed of light in given medium is 'v'.

Therefore,

Refractive Index of the given  medium (nm) = ${{Speed\,of\,light\,in\,air}\over {Speed\,of\,light\,in\,given\,medium\,}} = {c\over\upsilon}$

(b) Express the relation between the refractive index and speed of light in the medium. Refractive Index is the relative value of the speed of light of a medium with respect to the speed of light in vacuum, thus light will travel faster in the medium having lower value of refractive index.

Q.73 Show the path of ray of light when it enters obliquely

(a) from air to water

(b) from water to air

Some of the light is reflected along OE. Instead of continuing in a straight line along OF, the light ray entering the water is bent as it passes from air into water, taking the path OB.

The incident ray AO makes the angle AOC with the normal. Angle AOC is the angle of incidence. The refracted ray OB makes the angle DOB with the normal produced. Angle DOB is the angle of refraction.

When a ray enters the denser medium normal to the interface, no refraction occurs. When a ray enters the denser medium at an oblique angle, refraction does occur and the ray is bent toward the normal.

Let us now take a look into the nature of the refraction if the light passes obliquely from one medium into another of lower optical density. i.e., from water to air

Suppose the light source were at B in Figure 14-3. Light ray BO then meets the surface at point 0, and angle BOD is the angle of incidence. Of course some light is reflected at this interface. However, on entering the air the refracted portion of the light takes the path OA.

The angle of refraction in this case is angle COA. It shows that the light is bent away from the normal. When a light ray enters a medium of lower optical density at an oblique angle, the ray is bent away from the normal.

Q.74 What is the value of refractive index of vacuum?

The refractive index of vacuum is 1.

As refractive index $= {{Speed\,of\,light\,in\,vacuum} \over {Speed\,of\,light\,in\,medium}}$ therefore refractive index for vacuum will be $= {{Speed\,of\,light\,in\,vacuum} \over {Speed\,of\,light\,in\,vacuum}} = 1$

$Refractive{\rm{ }}index,n = {{Speed\,of\,light\,in\,vacuum\,or\,air} \over {Speed\,of\,light\,in\,medium}}$

Refractive index of medium 1 with respect to medium 2 :

${{Speed\,\,of\,\,light\,\,in\,\,medium\,\,2}\over {Speed\,\,of\,\,light\,\,in\,\,medium\,\,1}}$

${n_{12}} = {{{v_2}} \over {{v_1}}}$

Refractive index of medium 2 with respect to medium 1:

${{Speed\,\,of\,\,light\,\,in\,\,medium\,\,1}\over {Speed\,\,of\,\,light\,\,in\,\,medium\,\,2}}$

${n_{21}} = {{{v_1}} \over {{v_2}}}$

${n_{21}} = {1 \over {{n_{21}}}}$

Q.75 Define the ‘Principle of Reversibility of light’.

The retracing of light rays back to the path from where it started after the light had undergone multiple reflection or refraction is known is the principle of reversibility of light.

Q.76 Diamond has highest refractive index as 2.42. What does this value signifies?

It means that the speed of light in diamond is 1/2.42 times its speed in vacuum.

Lens

Q.77 What is lens? What are converging and diverging lens?

Lens is a transparent material formed by combining two surfaces either both spherical or one spherical and other plane.

There are two different types of lenses:

1. Convex or converging lens: These lenses are thicker at the centre and thinner at the ends. These are also called converging lens as these lenses converges the light rays falling on them.

These could be of three types:

•  Double convex lens

•  Plano-convex lens

•  Concavo- convex lens

2. Concave or diverging lens: These lenses are thinner in the middle and thicker at the ends. These are also called diverging lens as the light falling on these lenses gets diverge.

These could be of three types:

• Double concave lens

• Plano-concave lens

•  Convexo-concave lens

Q.78 Define:

(a) Focal length

(b) Centre of curvature

(d) Principle axis

(e) Optical Centre?

(a) Focal Length:- The distance between optical centre and principal focus is called focal length of a lens.

Focal length of a lens is half of the radius of curvature.

i.e., 2f = R    Or ,  f = R/2

This is the cause that the centre of curvature is generally denoted by 2F for a lens instead of C

(b) Centre of curvature :

Centre of curvature:The centre of sphere of part of which a lens is formed is called the centre of curvature of the lens. Since concave and convex lenses are formed by the combination of two parts of spheres, therefore they have two centres of curvature.

One centre of curvature is usually denoted by C1 and second is denoted by C2.

(c) Radius of curvature : The distance between optical centre and centre of curvature is called the radius of curvature, which is generally denoted by R.

(d)Principal Axis : Imaginary line that passes through the centres of curvature of a lens is called Principal Focus.

(e) Optical centre : The central point of a lens is called its Optical Centre. A ray passes through optical centre of a lens without any deviation.

Q.79 Where should the incident ray be directed so that the ray passing through concave lens after reflection becomes parallel to Principle axis?

The incident ray directed towards the focus, after refraction from the lens, becomes parallel to the principal axis. (Principal of reversibility of light)

Q.80 What are the rules for image formation in lenses?

The rules for image formation are-

• A ray passing through the optical centre (O) of the lens proceeds undeviated through the lens.

• A ray passing parallel to the principal axis after refraction through the lens passes or appears to pass through the focus(F). (By definition of the focus)

• A ray through the focus or directed towards the focus(F’), after refraction from the lens, becomes parallel to the principal axis. (Principal of reverssibility of light)

Q.81 With the help of a diagram explain the following terms in concave and convex lenses:

• Optical centre

•  Principle focus

(a) Optical centre :

Ray passing through the optical centre of convex and concave lens emerges in same direction without any deviation.

(b)Principle Focus :

A ray passing through principal focus emerges parallel to the principal axis after refraction from a convex lens.

A ray passing through the principal focus emerges parallel to the principal axis after diverging from a concave lens.

Q.82 Why is convex lens known as converging lens?

The light rays after bending from the convex lens meet at a point on the principal axis. In other words, these lenses converges the light rays falling on them.  Hence it is called converging lens.

Q.83 Define the lens formula.

The relation between distance of object (u), distance of image (ν) and focal length (f ) for a lens is called lens formula.

The lens formula is expressed as

Lens Formula

1/ν - 1/u = 1/f

Distance of object and image is measure from the optical centre of the lens. The sign for distance is given as per convention.

The lens formula given above is general and is valid in all situations for any spherical lens.

Q.84 What is meant by magnification?

The ratio of height of image and that of object or ratio of distance of image and distance of object gives magnification. It is generally denoted by 'm'.

If h is the height of the object and h′ is the height of the image given by a lens, then the magnification produced by the lens is given by,

m = Height of the Image / Height of the object = h' / h

Therefore,

Magnification (m) = ${{Height\,of\,image\left( {h'} \right)} \over {Height\,of\,object\left( h \right)}} = {{Distance\,of\,image\left( \nu\right)} \over {Distance\,of\,object\left(u\right)}}$

The positive (+) sign of magnification shows that image is erect and virtual while a negative (-) sign of magnification shows that image is real and inverted.

Q.85 Explain image formation by convex lens by placing objects in the following positions:

1. Object at infinity

2. Object beyond centre of curvature, C

3.Object at centre of curvature, C

4. Object between centre of curvature, C and principal focus, F

5. Object at principal focus, F

6. Object between principal focus, F and optical centre, O

(a) Object at infinity:-

Convex lens converge parallel rays coming from objet at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus F2.

Position of image: At F2

Nature of image: Real and inverted

Size of image: Point sized, highly diminished.

#### (b) Object beyond centre of curvature, C1 or 2F1:-

A diminished, real and inverted image is formed between principal focus, F2 and centre of curvature, C2 at the opposite side when an object is placed beyond C1 of a convex lens.

Position of image: Between 2F2 and F2

Nature of image: Real and inverted

Size of image: Diminished.

##### (c) Object at centre of curvature, C1 or 2F1:

A same sized, real and inverted image is formed at centre of curvature, C2 when object is placed at centre of curvature, C1 of a convex lens.

Position of image: At 2F2

Nature of image: Real and inverted

Size of image: Same sized.

###### (d) Object between centre of curvature, C1 and principal focus, F1:

An enlarged, real and inverted image is formed beyond centre of curvature, C2 when an object is placed between centre of curvature, C1 and principal focus, F1 of a convex lens.

Position of image: Beyond 2F2

Nature of image: Real and inverted

Size of image: Enlarged

(e) Object at principal focus, F1:-

An infinitely large, real and inverted image is formed at infinity when object is placed at principal focus, F1 of a convex lens.

Position of image: At infinity

Nature of image: Real and inverted

Size of image: Highly enlarged

(f) Between principal focus, F1 and optical centre, O:-

A virtual, erect and enlarged image is formed at the same side of lens, when an object is placed between principal focus, F1 and optical centre, O of a convex lens.

Position of image: Beyond 2F1

Nature of image: Virtual and erect

Size of image: Enlarged.

Rules for image formation by converging lenses.

Q.86 Explain the image formation by concave lens by placing the objects in the following positions:

(a) Object is at infinity

(b) Object is between optical centre, O and infinity

### (a) Object is at infinity:-

A highly diminished point sized, virtual and erect image is formed when object is at infinity by a concave lens at principal focus F1.

Position of image:- At F1

Nature of image: Virtual and erect

Size of image: Point sized, highly diminished.

#### (b) Object is between optical centre, O and infinity:

A diminished, virtual and erect image is formed between principal focus F1 and optical centre, O; when object is placed between optical centre and infinity of a concave lens.

Position of image:- Between F1 and O

Nature of image:- Virtual and erect

Size of image :- Diminished.

Rules for image formation by diverging lenses.

Q.87 What are the Sign conventions for lens:

##### Sign convention for lens:-

Sign convention for lens is similar to that of spherical mirror. Signs are taken left of the optical centre as negative, right of the optical centre as positive, above of the principal axis as positive and below of the principal axis as negative.

The new sign convention is known as New Cartesian Sign Convention. In this sign is taken negative towards left and taken as positive towards right at X-axis from origin.

The sign is taken as positive (+) above the origin point at Y-axis; and below the origin point as negative (-) at Y-axis.

Q.88 What are the sign conventions used to determine the positions and characters of the images formed by lenses?

1. The height 'h’ of the image is positive if the image is upright, with respect to the object, and negative if the image is inverted.

2. The magnification M of the image is positive if the image is upright, with respect to the object, and negative if the image is inverted.

3. The image distance q is positive if the image is real, and, therefore, located behind the lens, and negative if the image is virtual, and, therefore, located in front of the lens.

4. The focal length f of the lens is positive if the lens is converging, so that the image focus Fiis located behind the lens, and negative if the lens is diverging, so that the image focus Fi is located in front of the lens.

5. The front side of the lens is defined to be the side from which the light is incident.

Q.89 Give two uses of convex lens.

(i)Convex lens is used as an objective lens for telescopes.

(ii)Convex lens is used in cine projectors.

Q.90 Give two uses of concave lens.

(i) Concave lens is used in correcting short sightedness.

(ii) Concave lens is used as an eye lens for Galilean telescope

Q.91 What is a critical angle?

The angle of incidence in the denser medium for which the angle of refraction is 900.

Q.92 What is meant by ‘total internal reflection’? State two essential conditions for internal reflection to take place. Illustrate an application of total internal reflection:

(a) When light passes from one medium to another, it bends from its path which is called refraction. When a light ray passes from denser to rarer medium, at some angle of incidence it does not go out

The angle of incidence in the denser medium for which corresponding angle of refraction is 90 degree in the rarer medium is called the critical angle. This angle of incidence is denoted by C.

When the value of the angle of incidence becomes greater than the critical angel then the ray does not pass into the second medium (e.g., air) that is the ray of light no longer suffers refraction but all the rays having angle of incidence greater than the critical angel are totally reflected back in the denser medium (e.g., glass) obeying the laws of reflection. Such a reflection of light is called “total internal reflection”.

(b)Conditions for total internal reflection are-

1. The light ray must be travelling from optically denser medium to rarer medium.

2. The angle oof incidence must be greater than the critical angle.

3. Optical fiber communication uses the principle of total internal reflection for transferring data through optical fibres.

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