Refracting surface with a coating

JEE Advanced 2014 Paper 1, Question 9

A transparent thin film of uniform thickness and refractive index n_{1}=1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n_{2}=1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f_{1} from the film, while rays of light traversing from glass to air get focused at distance f_{2} from the film. Then

Rendered by

  1. \left|f_{1}\right|=3 R
  2. \left|f_{1}\right|=2.8 R
  3. \left|f_{2}\right|=2 R
  4. \left|f_{2}\right|=1.4 R

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