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  4. 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 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 f 1 from the film, while rays of light traversing from glass to air get focused at distance f 2 from the film. Then

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Q. 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. ThenPhysics Question Image

JEE AdvancedJEE Advanced 2014Ray Optics and Optical Instruments

Solution:

For air to glass
$ \frac{1.5}{f_{1}}=\frac{1.4-1}{R}+\frac{1.5-1.4}{R}$
$\therefore f_{1}=3 \,R$
For glass to air.
$ \frac{1}{f_{2}}=\frac{1.4-1.5}{-R}+\frac{1-1.4}{-R} $
$\therefore f_{2}=2\, R$