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

A
|f1|=3R
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B
|f1|=2.8R
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C
|f2|=2R
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D
|f2|=1.4R
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Solution

The correct options are
A |f1|=3R
C |f2|=2R
For air to glass,
1.5f1=1.41R+1.51.4Rf1=3R
For glass to air,
1f2=1.41.5R+11.4Rf2=2R.
Hence, the correct options are (a) and (c).

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