A transparent thin film of uniform thickness and refractive index n1 = 1.4 is coated on the convex s

Question

A transparent thin film of uniform thickness and refractive index n₁ = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n₂ = 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

Accepted Answer

As thickness of film is uniform, the effective power of the film is zero.
∴ We can find the answer just by considering glass-air interface.
In case-1,
Gives ⇒ f₁ = 3R
In case-2,
Gives
⇒ f₂ = 2R

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