Question

A thin spherical glass shell in air is filled with an unknown liquid. A parallel light beam is incident on the shell, and it is observed that the light is brought to focus on the surface of the shell directly opposite. What is the refractive index of the liquid?

The anwser is "n=2" but I'm not sure how this was calculated. I was thinking of using Snell's law and small angle approximation considering that this is a thin lens we're working with, but then again my brain doesn't physics very well so I have no idea if this should even be considered for this kind of question. Please help!

Thanks

Answer 1

Use the formula for thin walled lens which is
(n₂-n₁) / r = [n₁ / p] + [n₂ / q]
(n₂-1) / r= [1/oo] + [n₂/ 2r]

The first term on the left is very close to zero.
You can then solve for n₂ which will result to 2.