# Find index of refraction of a sphere given the beam path

MrMoose

## Homework Statement

A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n1 (see figure). (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b)What index of refraction, if any, will produce a point image at the center of the sphere.

## Homework Equations

n1/p + n2/i = (n2-n1)/r

## The Attempt at a Solution

n1 ~ 1.0 for air
i = 2r

Assuming that the factor n1/p -> 0 since the object is so far away that the light rays are parallel (is this assumption correct?)

(a) Substituting for n1 and i:

n2/2r = n2/r - 1/r

n2/2r - n2/r = -1/r

n2 (1/2r - 2/2r) = -1/r

n2(-1/2r) = -1/r

n2 = 2

This is the correct answer, but I want to make sure my assumption above was correct and I didn't just luck out.

(b) Using the same equation from part 2 above, but substituting i = r,

n2/r = n2/r - 1/r

0 = - 1/r

In order for this to be true, the sphere would have to be infinitely large so, realistically, there is no value of r that would place the image at the center of the sphere.

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