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.

Question

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 f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

TestHub · Accepted Answer

For air to glass 1.5 f 1 = 1.4 - 1 R + 1.5 - 1.4 R ∴ f 1 = 3 R For glass to air. 1 f 2 = 1.4 - 1.5 - R + 1 - 1.4 - R ∴ f 2 = 2 R

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