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Refraction of Light

Refraction of light and speed of light

Ankit went to an optician and noticed different types of spectacles there. He observed that while the glasses of some spectacles were relatively thicker in the middle, other glasses were thicker on the edge. The glasses of these spectacles are examples of lenses.

A lens is a transparent material bound by two curved surfaces. Lenses are broadly classified into two categories depending on their surfaces.

However, we will discuss only double spherical lenses here.

Convex lens

A convex lens is made by joining two spherical surfaces in such a way that it is thicker at the centre. Its thickness gradually reduces as we move towards the edge.

A convex lens has the ability to converge the light rays to a point that are incident on it. Thus, it is called a converging lens.

Concave lens

A concave lens is made by joining two curved surfaces in such a way that it is thinner at the centre. Its thickness gradually increases as we move towards the edge.

A concave lens has the ability to diverge a beam of light rays incident on it. Thus, it is called a diverging lens.

Differences between a spherical mirror and a lens

The following table lists some common differences between spherical mirrors and lenses

Spherical mirror

Spherical lens

Image is formed by reflection of light.

Image is formed by refraction of light.

A spherical mirror has only one focus.

A spherical lens has two foci.

The centre of the spherical mirror is termed as its pole.

The centre of the spherical lens is termed as its optical centre.

The second difference arises due to the fact that a lens has two spherical surfaces (i.e. it can be made from the arc of two spheres of equal radius).Therefore, light is refracted twice before it comes out of the lens.

Terms Associated with Lenses:

Optical centre

Optical centre is a point at the centre of the lens. It always lies inside the lens and not on the surface. It is denoted by ‘O’.

Centre of curvature

It is the centre point of arcs of the two spheres from which the given spherical lens (concave or convex) is made. Since a lens constitutes two spherical surfaces, it has two centers of curvature.

The distance of the optical centre from either of the centre of curvatures is termed as the radius of curvature.

Principal axis

The imaginary straight line joining the two centers of curvature and the optical centre (O) is called the principal axis of the lens.

Hold a convex lens and direct it against the sunlight. You will find a bright spot appear on the wall. Can you explain the formation of this bright spot? Light, after refracting through the lens, converges at a very sharp point. Try to obtain the brightest possible spot. Now, place a paper on the wall and observe what happens in the next few minutes.

Focus

The focus (F) is the point on the principal axis of a lens where all incident parallel rays, after refraction from the lens meet or appear to diverge from. For lenses there are two foci (F1 and F2) depending on the direction of incident rays.

The distance between the focus (F1 or F2) and the optical centre (O) is known as the focal length of the lens.

Refraction by Spherical Lenses

Refraction by a spherical lens can be categorized into three cases.

Case I. When the incident light ray is parallel to the principal axis

In this case, the refracted ray will pass through the second focus F2 for a convex lens, and appear to diverge from the first focus F1 for a concave lens.

Case II. When the incident light ray emerges from the first focus F1 of a convex lens, or appears to emerge from the second focus F2 of a concave lens

In this case, light after refraction from both the lenses will move parallel to the principal axis.

Case III. When the light ray passes through the optical centre (O) of a lens

In this case, the light ray will pass through both the lenses without suffering any deviation.

Chandu was surprised when he came to know that white light is actually a combination of lights of different colours.

On rainy days, you see a rainbow in the sky. You must have seen colours reflecting on the surface of a compact disc (CD) in the presence of sunlight. You might have wondered where these colours come from.

The common point among the above examples is the presence of sunlight. To understand these phenomena, it is necessary to learn about the composition of sunlight.

Composition of sunlight

Let us first go through an activity.

The seven coloured disc that you have seen in the activity is known as Newton Disc.

So, you have learned that light emitted by the sun is composed of seven different colours. These colours are red, orange, yellow, green, blue, indigo and violet.

You can remember the seven colours of sunlight by the mnemonic VIBGYOR. Each letter represents the initial letters of the colours.

Newton and his Prism

Isaac Newton (1642 − 1726) was one of the greatest physicists and mathematicians that the world has ever seen. He was the first scientist to resolve white sunlight into its component colours. He used a transparent optical object called prism, which is made of glass, to separate the seven colours of white light. He allowed sunlight to enter a dark room through a hole. He then placed a prism to obstruct sunlight inside the room. He saw a band of seven colours on the dark wall. He published a paper depicting his findings about the constituent colours of white light.

Try to obtain and observe the seven colours using a prism. Now, place a red transparent plastic sheet in front of sunlight. Are you able to see the seven colours? Perform similar experiments using other coloured transparent sheets. What do your findings suggest? Discuss the result with your friends.

On placing a red transparent sheet in front of sunlight, you observe that the spectrum of colours vanishes and only red-coloured light is obtained on the screen. Similarly, you will obtain only blue-coloured light on the screen for a blue transparent sheet and so on.

Try to observe the seven colours of sunlight on the surface of a soap bubble.

Take a wide tub filled with water and place it in sunlight. Observe the surface of water carefully. Is any colour of sunlight visible? Now, pour five to ten drops of petrol in water. Petrol will spread over the entire surface of water. Observe the water surface carefully. You will observe that the colours of a rainbow are present in the tub. Is it correct to infer that petrol can act as a prism? Discuss and confirm this with your teacher.

A rainbow appears in the sky only when it rains. Which substance or object acts as a prism to separate the various components of sunlight to form a rainbow?

Prism A transparent refracting medium which is bounded by five plane surfaces and having a triangular cross section is known as prism. The figure below shows the passage of light through a triangular prism ABC.

The angles of incidence and refraction at first face AB are ∠i and ∠r1.

The angle of incidence at the second face AC is ∠r2 and the angle of emergence ∠e.

δ is the angle between the emergent ray RS and incident ray PQ and is called the angle of deviation.

Here, ∠PQN = i

∠RQO = r1

∠QRO = r2

∠KTS = δ

∠TQO = i and ∠RQO = r1, we have

∠TQR = i − r1

∠TRO = e and ∠QRO = r2

∠TRQ = e − r2

In triangle TQR, the side QT has been produced outwards. Therefore, the exterior angle δ should be equal to the sum of the interior opposite angles.

i.e, δ= ∠TQR + ∠TRQ = (i − r1) + (e − r2)

δ = (i + e) − (r1+ r2) …(i)

In triangle QRO,

r1+ r2+ ∠ROQ = 180° …(ii)

From quadrilateral AROQ, we have the sum of angles (∠AQO + ∠ARO = 180°). This means that the sum of the remaining two angles should be 180°.

i.e , ∠A + ∠QOR = 180° [∠A is called the angle of prism]

From equations (i) and (ii),

r1+ r2 = A (iii)

Substituting (iii) in (i), we obtain

δ = (i + e) − A

A+δ=i+e

If the angle of incidence is increased gradually, then the angle of deviation first decreases, attains a minimum value (δm), and then again starts increasing.

When angle of deviation is minimum, the prism is said to be placed in the minimum deviation position.

There is only one angle of incidence for which the angle of deviation is minimum.

When

δ = δm [prism in minimum deviation position],

e = i and r2 = r1 = r …(iv)

∵ r1+r2=A

From equation (iv), r + r = A

r=A2<

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