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A ray of ligh...

Question

A ray of light passing from air through an equilateral glass prism undergoes minimum deviation when the angle of incidence is $\frac{3}{4}$ th of the angle of prism. Calculate the speed of light in the prism.

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Solution

Here, Angle of prism, $A = 60^{o}$

Angle of incidence, i= $\frac{3}{4} \times 60$

i+e=A+ $δ$

e is emergence angle

where $δ$ is deviation angle

At minimum deviation $δ = δ_{m i n}$

i=e

2i=A+ $δ_{m i n}$

$2 \times 45 = 60 + δ_{m i n}$

$δ_{m i n} = 30$

By prism law,

$μ = \frac{sin \frac{A + δ_{m i n}}{2}}{sin \frac{A}{2}}$

$μ = \frac{sin \frac{60 + 30}{2}}{sin \frac{60}{2}} = \frac{2}{\sqrt{2}} = 1.41$

Let v be velocity of light in prism

$v = \frac{c}{μ} = \frac{3 \times 10^{8}}{1.41}$ = $2 \times 10^{8}$ m/s

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