The angle of a prism is ‘ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surfac

Question

The angle of a prism is &lsquo; A &rsquo;. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index &#956; , of the prism is:

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Correct answer: B. 2 cos ⁡ A

To retrace its path light rays should fall normally on the reflecting surface. So r 2 = 0 ⇒ r 1 = A - r 2 ⇒ r 1 = A Now applying snell rule between incident ray and refracted ray. 1 sin ⁡ 2 A = n sin ⁡ A ⇒ 2 sin ⁡ A cos ⁡ A = n sin ⁡ A ⇒ n = 2 cos ⁡ A

The angle of a prism is ‘ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ , of the prism is:

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More from Ray Optics

The angle of a prism is &lsquo; A &rsquo;. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index &#956; , of the prism is:

Options

Correct answer

Step-by-step solution

More from Ray Optics

The angle of a prism is ‘ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ , of the prism is: