Physics

(a) The velocity of light in diamond is 121000 km/s. What is its refractive index?
(b) With the help of a labelled diagram, show that the apparent depth of an object such as a coin in water is less than its real depth.

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(a) Given,

velocity of light in diamond = 121000 kms^-1

To convert kms^-1 into ms^-1, we multiply by 1000

121000 x 1000 ms^-1 = 121 x 10⁶ ms^-1

Speed of light in air, c = 3 × 10⁸ ms^-1

As we know,

$μ = \dfrac{\text{Speed of light in vacuum or air (c) }}{\text {Speed of light in diamond (V)}} \\[0.5em]$

Substituting the values in the formula above we get,

$μ = \dfrac{ 3 \times 10^8 } {121 \times 10^6} \\[0.5em] μ = \dfrac{ 3 \times 10^8 } {1.21 \times 10^8} \\[0.5em] μ = 2.48 \\[0.5em]$

Hence, refractive index = 2.48

(b) Below labelled diagram, shows that the apparent depth of a coin in water is less than its real depth:

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