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Q.

The velocity of light in glass is $2 \times 1 0^{8} m / s$ and that in the air is $3 \times 1 0^{8} m / s$ . By how much would an ink dot appear to be raised, when covered by a glass plate 6.0 cm thick?

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a

2 cm

b

4 cm

c

5 cm

d

8 cm

answer is A.

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Detailed Solution

Concept: The ratio of the speed of light in a vacuum to that in a second medium with a higher density is used to compute the refractive index (also known as the index of refraction). In mathematical formulae and descriptive writing, the letter n or n' is most frequently used to represent the refractive index variable.
By dividing the light's velocity in glass and in air, we can determine the refractive index.
The velocity of light in glass is

2 \times 1 0^{8} m / s

and that in the air is

3 \times 1 0^{8} m / s

n = \frac{Velocity of light in air}{Velocity of light in glass}

n = \frac{3 \times 1 0^{8}}{2 \times 1 0^{8}}

n = 1.5

Refractive index

= \frac{Real depth}{Apparent depth}

1.5 = \frac{6}{Apparent depth}

Apparent depth = 4
Ink dot looks to be lifted by 6-4 =2 cm as a result.
Hence, the correct answer is option 1

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