Question 378: Ray Optics

Question

A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $$\mu $$1 and $$\mu $$2 and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

Accepted Answer

Equivalent focal length is $${1 \over {{f_{eq}}}} = {1 \over {{f_1}}} + {1 \over {{f_2}}}$$
$$ \Rightarrow $$ $${1 \over {{f_{eq}}}}$$ = $$\left( {{\mu _1} - 1} \right)\left( {{1 \over \infty } - {1 \over { - R}}} \right)$$ + $$\left( {{\mu _2} - 1} \right)\left( {{1 \over { - R}} - {1 \over \infty }} \right)$$
$$ \Rightarrow $$ f
eq
= $${R \over {\left( {{\mu _1} - {\mu _2}} \right)}}$$

Answer

$${R \over {\left( {{\mu _1} - {\mu _2}} \right)}}$$

Answer

$${{2R} \over {\left( {{\mu _2} - {\mu _1}} \right)}}$$

Answer

$${R \over {2\left( {{\mu _1} + {\mu _2}} \right)}}$$

Answer

$${R \over {2\left( {{\mu _1} - {\mu _2}} \right)}}$$

Ray Optics

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