Question

Obtain the lens maker’s formula for a lens of refractive index n₂ which is separating two media of refractive indices n₁ and n₃ on the left and right respectively.

Answer 1

`"n"_2/"v" - "n"_1/"u" = ("n"_2 - "n"_1)/"R"`

Refraction at 1^st surface-

`"n"_2/"v'" - "n"_1/"u" = ("n"_2 - "n"_1)/"R"_1`    ...(1)

Refraction at 2^nd surface-

`"n"_3/"v" - "n"_2/"v'" = ("n"_3 - "n"_2)/"R"_2`   ...(2)

Add equation (1) and (2)

`"n"_3/"v" - "n"_1/"u" = ("n"_2 - "n"_1)/"R"_1 + ("n"_3 - "n"_2)/"R"_2`