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Angle of prism is A and its one surface ...

Angle of prism is `A` and its one surface is silvered. Light rays falling at an angle of incidence `2 A` on first surface return back through the same path after suffering reflection at second silvered surface. Refraction index of the material of prism is

A

` 2 sin A `

B

`2 cos A `

C

`2 tan A `

D

`2 sin"" (A)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
PQ is the incident ray and the refracted ray QR is incident normally on the silvered surface AC. Hence refraces its path .

In `Delta AQR , angleAQR = theta =90 - A`
`therefore angle` of refraction `r + theta = 90^(@)`
`therefore r = 90 - theta = 90 - 90 + A = A`
`therefore n= (sin i)/(sin r) = (sin 2 A)/(sin A)`
`= (2 sin A cos A)/(sin A) = 2 cos A`
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