A ray of light is incident at an angle of incidence \(60º\) on the glass slab of refractive index \(\sqrt 3.\) After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \(4\sqrt 3.\) cm. The thickness of the glass slab is ______ cm.
Correct Answer: 12
Solution and Explanation
\(1 \times sin \ 60\degree = \sqrt 3 \times sin\ r\)
\(⇒ r = 30\degree\)
∴ \(I_1 = 4\sqrt 3 \times 2\)
\(= 8 \sqrt 3\ cm\)
∴ Thickness, \(t = l_1 cos\ 30\degree\)
\(= 8 \sqrt 3 \times \frac {\sqrt 3}{2}\)
\(= 4 × 3\)
\(= 12\ cm\)
So, the answer is \(12\ cm\).
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Concepts Used:
Refraction of Light
Refraction is the bending of a wave when it enters a medium where its speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.
If you ever observe a pencil dipped into water, you’ll notice that it seems to be tilted at an angle at the interface of air and water, or the bottom of a tub or a tank that contains water seems to be raised. This phenomenon is caused due to the process of refraction of light. Refraction of light is the bending of the light wave, passing from one medium to another, which is caused due to the difference in the density of the two mediums.
Reason behind Refraction
The main cause of refraction is the variation in the velocity of the light when it enters different mediums. The speed of light in the air is faster than that of water. So, the speed of the light increases when it travels from water to air, and similarly, the speed decreases when it travels from air to water.
In the below figure, it is shown why the printed alphabets appear to have risen when seen through a glass slab. This is because when the light travels from air to glass, the speed gets reduced and the light moves toward the normal, that is the light rays move towards the NN’ normal from its original path. Likewise, when the light ray travels from glass to air, its speed gets increased and it moves away from the normal.
Refraction of Light in Reality
- Twinkling of the stars - The atmosphere is composed of areas of the thick and thin atmosphere. When one looks at the stars at night, the light passing through these different layers of the atmosphere from the stars reaches our eyes and therefore the stars appear to twinkle.
- As the light travels from the bottom to the top, the light coming from the pool bends due to refraction and thus the swimming pool always looks shallower than it really is.
- Due to the refraction of light, white light when passed through a prism splits into red, orange, yellow, green, blue and violet colours.
Laws of Refraction of Light
There are two Laws of Refraction. They are:
- The incident ray, the normal to the interface of two media, and the refracted ray, all lie on the same plane.
- Snell's Law: Snell’s law states that the ratio of the sine of the incident angle to the sin of refracted is constant. It describes the relationship between angles of refraction and angles of incidence.
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