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KVPY2017PhysicsRay Optics

It was found that the refractive index of material of a certain prism varied as 1.5+0.004 / ² , where is the wavelength of light used to measure the refractive index. The same material was then used to construct a thin prism of apex angle 10^ . Angles of minimum deviation ( _ m ) of the prism were recorded for the sources with wavelengths ₁ and ₂ respectively. Then

Options

  1. A_ m ( ₁ ) < _ m ( ₂ ) if ₁ < ₂ .
  2. B_ m ( ₁ )> _ m ( ₂ ) if ₁> ₂
  3. C_ m ( ₁ )> _ m ( ₂ ) if ₁ < ₂ .
  4. D_ m is the same in both the cases.

Correct answer

C. _ m ( ₁ )> _ m ( ₂ ) if ₁ < ₂ .

Step-by-step solution

n = i r = ( _ m + A 2 ) ( A 2 ) 1.5+ 0.004 ² = ( _ m + A 2 ) ( A 2 ) _ m 1 _ m ( ₁ )> _ m ( ₂ ) if ₁ < ₂

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