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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 = (n2n1)/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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