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

2 sinA

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2 cosA

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\frac{c o s A}{2}

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tanA

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Solution

The correct option is B 2 cosA

Apply snells law at PQ
$μ_{1}$ sin 2A $= μ_{2}$ sin A
$μ_{1}$ 2 sinA cosA = $μ_{2}$ sinA
$1 \times 2$ cosA = $μ_{2}$
$μ_{2}$ = 2 cosA

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

Angle of prism is ‘A’ and its one surface is silvered. Light rays falling at an angle of 2A and travels through the same path after suffering reflection at second silvered surface. The refractive index of the material of the prism is

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

The correct option is B 2 cosA Apply snells law at PQ μ1 sin 2A =μ2 sin A μ1 2 sinA cosA =μ2 sinA 1×2 cosA =μ2 μ2 = 2 cosA

The correct option is B 2 cosA

Apply snells law at PQ
$μ_{1}$ sin 2A $= μ_{2}$ sin A
$μ_{1}$ 2 sinA cosA = $μ_{2}$ sinA
$1 \times 2$ cosA = $μ_{2}$
$μ_{2}$ = 2 cosA