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.
![](https://imagex.cdn.examgoal.net/1ktqs5zcv/43fb95d9-ffe2-4768-b9a2-61aa46818b00/a12a15e0-190a-11ec-9e1c-4f8f7e7dad5b/file-1ktqs5zcw.jpeg)

Accepted Answer

${1 \over {{f_1}}} = ({\mu _1} - 1)\left( {{1 \over R}} \right)$
${1 \over {{f_2}}} = ({\mu _2} - 1)\left( {{1 \over R}} \right)$
${1 \over {{f_1}}} + {1 \over {{f_2}}} = {1 \over {{f_{eq}}}} = {{({\mu _1} - 1) - ({\mu _2} - 1)} \over R}$
${1 \over {{f_{eq}}}} = {{({\mu _1} - {\mu _2})} \over R}$
${R \over {{f_{eq}}}} = ({\mu _1} - {\mu _2})$
![](https://imagex.cdn.examgoal.net/1ktqs6uv3/3de38818-02c3-492c-96bf-12028c7281c7/b980b4f0-190a-11ec-9e1c-4f8f7e7dad5b/file-1ktqs6uv4.png)

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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