Question

7. One face of prism with refracting angle 37° is
coated with silver. A light ray incident on other face
at angle 60° is refracted and reflected back from
the silver coated face such that it retraces its path.
The refractive index of prism is
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Answer 1

question: one face of prism with refracting angle 37 degree is coated with silver. a light Ray incident on other face at angle 60 degree is refracted and reflected back from the silver coated face such that it retraces it's path . the refractive index of prism is

answer: use snell s law

Answer 2

Answer:

The refractive index of the prism is $\frac{5 }{2\sqrt{3} }$.

​Explanation:

From the snell's law, we have,

$\mu_1sini=\mu_2sinr$             (1)

Where,

μ₁=refractive index of the medium in which light is present

i=angle of incidence

μ₂=refractive index of the medium in which light is supposed to enter

r=angle of refraction

From the question we have,

μ₁=1           (This medium is air)

i=60°

r=37°

By substituting the required values in equation (1) we get;

$1\times sin60\textdegree=\mu_2\times sin37\textdegree$              

$1\times \frac{\sqrt{3} }{2} =\mu_2\times \frac{3}{5}$

$\mu_2=\frac{5\sqrt{3} }{2\times 3}$

$\mu_2=\frac{5 }{2\sqrt{3} }$

Hence, the refractive index of the prism is $\frac{5 }{2\sqrt{3} }$.

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