Question

Two identical thin plano-convex glass lenses (refractive index ) each having radius of curvature of are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index . The focal length of the combination is

A

B

C

D

Hard
Solution
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Correct option is D)

Here the light passes through three refracting media, as shown in the figure.
Media has a refractive index and radius of curvature . While medium has a refractive index of and it acts as a concave lens.
Let the focal length of the three media be .
Applying the lens makers formula

For media ,
since it is a plano convex lens.


For media ,

For media ,
Since media are similar we can write


For applying the formula for equivalents lenses,



Hence the correct answer is option (D).

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