Light Energy

Both A and R are true and R is not the correct explanation of A

Explanation

The Assertion is true: when white light passes through a prism it separates into its constituent colours due to dispersion—different colours travel with different speeds in glass and are refracted by different amounts.
The Reason is also true: white light is indeed a mixture of the seven spectral colours (violet, indigo, blue, green, yellow, orange and red).
However, merely stating that white light is a mixture does not explain why the prism causes the colours to separate; the key point is the wavelength-dependent refractive index of the prism material. Therefore, the Reason is not the correct explanation of the Assertion.

Assertion is true but reason is false

Explanation

Assertion (A) is true because the bottom of a pond appears shallower than its actual depth due to refraction of light from water to air.

Reason (R) is false because water is a denser medium as compared to air so the light rays coming from the bottom of the pond bend away from the normal as they pass from water to air due to increase in speed.

Both A and R are true and R is the correct explanation of A

Explanation

Assertion (A) is true because a concave mirror forms real as well as virtual images depending on the position of the object relative to the mirror's focal point.

Reason (R) is true because a concave mirror forms real and virtual images such that if the image is virtual then the object is very close to the mirror before its focus and if the image is real then the object is at focus or beyond it.

So, here reason clearly explains the assertion that concave mirror forms real and virtual images depending on the position of the object relative to the mirror's focal point.

Assertion is true but reason is false

Explanation

The assertion is correct: convex mirrors are installed in large showrooms, department stores and at road intersections as vigilance or security mirrors because they provide a wide field of view.

The reason is incorrect: a convex mirror always forms a virtual, erect and diminished image of the object, not a magnified one. The diminished image allows a larger area to be observed in the mirror, which is why convex mirrors are useful for surveillance.

(a) Water is optically denser than air.

(b) Air is optically rarer than glass.

(c) When a ray of light travels from water to air, it bends away from the normal.

(d) When a ray of light travels from air to glass, it bends towards the normal.

(e) Refractive index of water is 4/3, so the apparent depth is 3/4th of the real depth.

(f) The splitting of white light into its constituent colours is called dispersion.

(g) A concave mirror is obtained on silvering the outer surface of a part of a hollow glass sphere.

(h) Radius of curvature of a spherical mirror is two times its focal length.

(i) The angle of incidence for a ray of light passing through the centre of curvature of a spherical mirror is 0°.

(j) A convex mirror always forms a virtual image.

(k) A concave mirror forms a virtual image for an object placed between pole and focus.

Experiment to show that a light ray bends when it passes from one transparent medium into another transparent medium.

1. Take an empty beaker and a pencil. Place the pencil ABC obliquely in the beaker.
2. Look at the pencil from side. It appears straight as shown in figure (a).
3. Now pour water into the beaker up to its brim.

Pencil appears to be bent as ABD at the surface of water as shown in the figure (b).

The light ray coming from the tip C of the pencil bends at the surface of water as it enters in air and it appears to be coming from point D. Due to refraction of light from water to air, the pencil ABC appears as ABD.

This shows that when a ray of light passes from one transparent medium into another transparent medium it bends.

The ray diagram showing the apparent depth of a vessel full of water is given below:

The real depth of water is AO but when viewed obliquely from above, its depth appears to be AI due to refraction of light from water to air.

(a) When light ray AO passes from air (rarer medium) to water (denser medium), it bends towards the normal as shown below.

(b) When light ray AO travels from water (denser medium) to air (rarer medium), it bends away from the normal as shown in the diagram below.

(c) When light ray AO is incident normally to the surface, it passes undeviated as shown in the figure below.

Below figure shows the refraction of a light ray from water to glass:

AO — incident ray
i — angle of incidence
r — angle of refraction

The completed diagram showing the ray of light till it emerges out of the slab is given below :

AO — incident ray
OB — refracted ray
BC — emergent ray

A prism is a transparent medium bounded by five plane surfaces with a triangular cross section.

In symbol form it is represented by the triangle ABC :

The refraction of a light ray through a prism is shown below.

The light ray PQ of a single colour is incident obliquely on the surface AB of the prism. As the ray PQ moves from air (rarer) to glass (denser), it bends towards normal and travels as refracted ray QR. The refracted ray QR at the face AC of the prism again undergoes refraction (bends away from the normal) as it moves from glass (denser) to air (rarer) and emerges out as ray RS (emergent ray) from the prism.

Dispersion of a white light into its constituent colours by a prism is shown in the below figure.

White light splits up into seven constituent colours after passing through a prism. These seven colours VIBGYOR arranged from bottom to top are seen on the screen.

The two kinds of spherical mirrors are:

1. Concave mirror
2. Convex mirror

Figure of concave and convex mirror is shown below:

(a) Pole — The geometric centre of the spherical surface of the mirror is called the pole of the mirror. It is represented by the symbol P.

(b) Centre of curvature — The centre of curvature of a mirror is the centre of the sphere of which the mirror is a part. It is represented by the symbol C.

(c) Radius of curvature — The radius of curvature of a mirror is the radius of the sphere of which the mirror is a part. It is represented by symbol R.

(d) Principal axis — It is a straight line joining the pole of the mirror to its centre of curvature.

The focus (F) of a concave mirror is a point on the principal axis at which the light rays incident parallel to the principal axis, meet (converge) after reflection from the mirror.

The focus (F) of a convex mirror is a point on the principal axis at which the light rays incident parallel to the principal axis, appear to meet after reflection from the mirror.

The distance of the focus from the pole of the mirror is called the focal length of the mirror.

(a) A beam of light incident parallel to the principal axis of a concave mirror, after reflection meets at a point called focus of the mirror.

(b) A beam of light incident parallel to the principal axis of a convex mirror, after reflection appears to meet at a point called focus of the convex mirror.

The completed diagrams with focus marked are shown below :

C — Centre of curvature,
F — Focus,
P — Pole

Ray 1 passing through the focus of a concave mirror gets reflected parallel to the principal axis.

Ray 2 passing through the centre of curvature of a concave mirror is reflected along its own path.

Ray 1 appearing to pass through the focus of a convex mirror gets reflected parallel to the principal axis.

Ray 2 directed in the direction of centre of curvature of a convex mirror is reflected along its own path.

The two convenient rays that are chosen to construct the image formed by a spherical mirror for a given object are:

1. A ray that passes through the center of curvature — A line joining the centre of curvature to any point on the surface of mirror is normal to the mirror at that point, therefore a ray AD passing through the center of curvature C (or appearing to pass through through the centre of curvature C) is incident normally on the spherical mirror.
   Since it's angle of incidence is zero, therefore the angle of reflection will also be zero and the ray AD gets reflected along it's own path DA as shown below:

2. A ray parallel to the principal axis — A ray of light AD incident parallel to the principal axis, after reflection passes either through the focus F(in a concave mirror) or will appear to come from the focus F (in a convex mirror) along DB as shown below:

Nature — Image is real and inverted.

Position — The image is formed between the centre of curvature and focus of the concave mirror.

Size — The size of the image is smaller than that of the object.

Nature — Image is real and inverted.

Position — The image is formed at the centre of curvature of the concave mirror.

Size — The size of image and object is the same.

Nature — Image is real and inverted.

Position — The image is formed beyond centre of curvature of the mirror.

Size — The size of image is bigger than that of object.

Nature — The image is virtual and erect.

Position — The image is formed behind the mirror.

Size — The size of image is bigger than that of object.

Nature — Image is virtual and erect.

Position — The image is formed behind the mirror between focus and pole of the convex mirror.

Size — Image is diminished in size.

As the object is moved away from the mirror, the image moves towards the focus and the size decreases to a point.

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

(b) In convex mirror for the object placed at finite distance, the image formed is always virtual, erect, diminished and it is formed between pole and focus of the mirror.

The object should be placed between the pole and focus of the concave mirror to obtain a virtual image of the object.

A convex mirror diverges the incident light rays and always form a small, erect image between its pole and focus. This enables the driver to use it as a rear view mirror so that he could able to see all the traffic behind him approaching the mirror. It has wider field of view than a plane mirror.

3 x 10⁸ m s^-1

Reason — Speed of light in air or vacuum is fastest i.e. 3 x 10⁸ m s^-1

bends towards the normal

Reason — When light ray passes from rarer to denser medium speed of light decreases so it bends towards the normal.

angle of refraction

Reason — Angle of refraction is the angle formed between the normal and refracted ray.

dispersion

Reason — Dispersion is the property of splitting of white light into its seven constituent colours.

VIBGYOR

Reason — The order of seven colours in the spectrum of sunlight is VIBGYOR i.e. violet, indigo, blue, green, yellow, orange and red, respectively.

retraces its own path

Reason — A ray of light passing through the centre of curvature is incident normally on the spherical mirror and its angle of incidence and angle of reflection is zero so the light ray retraces its own path.

10 cm

Reason — Focal length is half of radius of curvature, so it will be 10 cm.

erect and diminished

Reason — Image formed by a convex mirror is always erect, virtual and diminished.

at the centre of curvature

Reason — If the object is placed at the centre of curvature of concave mirror the image formed is real, inverted and of the same size as that of object.

as a rear view mirror by a driver

Reason — A convex mirror always forms erect and small images and this fact enables to use it as a rear view mirror so that the driver can see all the traffic behind him.

(a) The speed of light in air is 3 x 10⁸ m s^-1.

(b) The speed of light in water is 2.25 x 10⁸ m s^-1.

(c) The speed of light in glass is 2 x 10⁸ m s^-1.

A medium is said to be denser if the speed of light in it decreases, while it is said to be rarer if the speed of light in it increases.

Water is optically denser than air because speed of light in water (2.25 x 10⁸ m s^-1) is less than speed of light in air (3 x 10⁸ m s^-1).

Air is optically rarer than glass as speed of light is more in air (3 x 10⁸ m s^-1) than the speed of light in glass (2 x 10⁸ m s^-1).

The change in direction of path of light when it passes from one optically transparent medium to another is called refraction of light.

(a) Incident ray — The ray of light falling on the surface separating the two media is called the incident ray.

(b) Refracted ray — The ray of light traveling in the other medium in the changed direction is called the refracted ray.

(c) Angle of incidence — The angle between the incident ray and the normal is called the angle of incidence (i).

(d) Angle of refraction — The angle between the refracted ray and the normal is called the angle of refraction (r).

When a ray of light falls normally on a glass slab the angle between incident ray and normal is 0°. So, the angle of incidence is 0°.

When a ray of light travels from a rarer medium to a denser medium, it bends towards the normal because the speed of light decreases in denser medium.

When a ray of light travels from a denser medium to a rarer medium, it bends away from the normal because the speed of light increases in the rarer medium.

The splitting of white light into its constituent colours while passing through a prism is called dispersion of light.

Spectrum is the coloured band obtained on a screen on passing the white light through a prism. The various colours present in the spectrum of sunlight are violet, indigo, blue, green, yellow, orange and red.

The two laws of reflection of light are:

1. The angle of incidence i is equal to the angle of reflection r.
2. The incident ray, the reflected ray and the normal, all lie in the same plane.

A spherical mirror is made by silvering a part of a hollow glass sphere. The surface on which silvering is done is called the silvered surface and the reflection of light takes place from the other surface known as the reflecting surface.

The mirror used is a concave mirror. The beam of light is incident parallel to the principal axis of the concave mirror. After reflection, the beam converges to a point called the focus of the concave mirror.

The mirror used is a convex mirror. The beam of light is incident parallel to the principal axis of the convex mirror. After reflection, the beam of light diverges and appear to meet at a point called the focus of the convex mirror.

A ray passing through the centre of curvature of a spherical mirror is reflected along its own path.
A line joining the centre of curvature to any point on the surface of mirror is always normal to it. Thus, a ray passing through the centre of curvature is incident normally on the spherical mirror. Its angle of incidence is zero, therefore, the angle of reflection is also zero. It means that the ray gets reflected along its own path.

The focal length of a spherical mirror is half of its radius of curvature.

Focal length = $\dfrac{\text{1}}{\text{2}}$ x Radius of curvature

Convex mirror always forms an erect and virtual image. The image size is always smaller as compared to that of the object.

Concave mirror forms an erect, virtual and enlarged image of an object. The object should be placed between the pole and focus of the concave mirror.

A real image is formed when the reflected rays actually meet at a point. It can be obtained on a screen.

Concave mirror is used to obtain the real image of an object. If the object is located at any position except between pole and focus of the concave mirror than the image formed is real.

The two uses of a concave mirror are:

1. It is used as a shaving mirror.
2. It is used as a doctor's head mirror.

The two uses of a convex mirror are:

1. It is used as a rear view mirror.
2. It is used as a reflector in street lamps.

(a) Concave mirror is used to obtain a real and enlarged image when object is placed between its centre of curvature and focus.

(b) Concave mirror is used to obtain a virtual and enlarged image when object is placed between its focus and pole.

(c) Concave mirror is used to obtain a real and diminished image when object is placed beyond its centre of curvature.

(d) Convex mirror produces a virtual and diminished image.

The below ray diagram shows why a coin appears raised when placed in a vessel filled with water:

When water is poured in the vessel, the ray of light from point A of the coin, travelling in a straight line changes its direction (i.e. it bends) at the surface of water and reaches the eye. The ray now appears to come from point B instead of point A to our eye. So, the coin appears to be raised from position A to position B.

A straight stick partly dipped in water obliquely, appears to be bent at the surface of water due to refraction of light. The light rays coming from the tip C of the stick, at the surface of water undergoes refraction and bends away from the normal and appears to us as coming from point D (as shown in figure). Due to refraction of light from water to air the pencil ABC appears to be bent as ABD at the surface of water.

The upper atmospheric layers are warmer than the layers near the surface of the earth before sunrise and after sunset, so the layers near the earth's surface are more denser than upper layers. When sun is below horizon the rays of sun passes from rarer to denser medium and suffers refraction by bending towards the normal. Due to continuous bending of light rays the sun appears to be above horizon. So the sun is seen before the sunrise and after the sunset.

Sometimes, in deserts, an inverted image of a tree is seen which gives a false impression of water under the tree. This is called a mirage.

Mirage is formed due to the refraction of light. In a desert, during the day-time, the hot sand rapidly heats the layers of air in contact with it. As a result, the layers of air near the ground are rarer and the successive upper layers are denser than those below them.

The light rays from sun after reflection from the top of a tree travel from denser (cold upper layers of air) to rarer medium (warmer lower layer of air) and undergo refraction bending away from the normal. On successive refraction, the angle of refraction increases and the angle of incidence of ray going from denser to rarer medium also increases till a stage is reached when the angle of refraction becomes 90°. On further increase in angle of incidence the light ray is not refracted but is reflected. This reflected ray now travels from rarer to denser layer and bends towards the normal at each refraction. On reaching the eye of the observer, an inverted image of the tree is seen. Thus, it gives a false impression of a pool of water in front of the tree.

The disc appears white when rotated rapidly. The reason is that seven colours violet, indigo, blue, green, yellow, orange and red are the constituent colours of white light. When these colours are combined they produce the white colour effect.

(a) Concave mirror is used by a dentist because if a parallel beam of light is incident on a concave mirror, it converges the beam to the focus. This enables the dentist to concentrate light on small area to be examined like teeth.

(b) A convex mirror is used as a street light reflector because it diverges the light rays incident on it.

(a) False
Correct Statement — Water is optically rarer than glass.

(b) False
Correct Statement — A ray of light when passes from glass to air, bends away from the normal.

(c) False
Correct Statement — The speed of light is less in glass than in water.

(d) True

(e) True

(f) False
Correct Statement — The direction of light changes from its initial path when passing through different media.

(g) False
Correct Statement — The angle formed between the normal and the refracted ray is known as the angle of refraction.

(h) True

(i) False
Correct Statement — Image is formed by a mirror due to reflection of light.

(j) True

(k) False
Correct Statement — A concave mirror is used as a shaving mirror.

(l) False
Correct Statement — The focal length of a convex mirror is half of its radius of curvature.

(m) True

(n) True