Question 122: Ray Optics

Question

Curved surfaces of a plano-convex lens of refractive index $$\mu$$
1
and a plano-concave lens of refractive index $$\mu$$
2
have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

Accepted Answer

$${1 \over {{f_1}}} = ({\mu _1} - 1)\left( {{1 \over R}} \right)$$
$${1 \over {{f_2}}} = ({\mu _2} - 1)\left( {{1 \over R}} \right)$$
$${1 \over {{f_1}}} + {1 \over {{f_2}}} = {1 \over {{f_{eq}}}} = {{({\mu _1} - 1) - ({\mu _2} - 1)} \over R}$$
$${1 \over {{f_{eq}}}} = {{({\mu _1} - {\mu _2})} \over R}$$
$${R \over {{f_{eq}}}} = ({\mu _1} - {\mu _2})$$

Answer

$${1 \over {{\mu _2} - {\mu _1}}}$$

Answer

$${\mu _1} - {\mu _2}$$

Answer

$${1 \over {{\mu _1} - {\mu _2}}}$$

Answer

$${\mu _2} - {\mu _1}$$

Ray Optics

Curved surfaces of a plano-convex lens of refractive index $\mu 1 and a plano-concave lens of refractive index \mu$ 2 have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

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