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What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

Options

  1. An < c o s e c A 2
  2. Bn < sec ⁡ A 2
  3. Cn > sec ⁡ A
  4. Dn > c o s e c A 2

Correct answer

D. n > c o s e c A 2

Step-by-step solution

Consider the situation shown in figure. Light rays P Q is incident on the face A B . It goes along Q R and then along R S . Here, i = angle of incidence at the face A B r 1 = angle of refraction through A B r 2 = angle of incidence at A C n = refractive index of the material of the prims. For the prism, we have r 1 + r 2 = A .....(i) Now for light not to emerge from the face A C , r 2 > C Similarly for no emergence from the face A B , r 1 > C ⇒ r 1 + r 2 > 2 C Here, C is critical angle. ⇒ A > 2 C ∵ r 1 + r 2 = A ⇒

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