Homework Help: Spherical Refraction Surfaces. (I'm confused as to how you get the answer.

1. Mar 22, 2009

afcwestwarrior

A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere.

Here's the equation you use to find the index of refraction of the sphere.

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

P (object distance or laser distance) = infinity (makes sense)

i (image distance) = 2r

r = radius of curvature

n1 (object's side refraction index) = 1.000 (air)

n2 (refractive index of the sphere ) = ?

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

somehow 1 / infinity goes away

so it becomes
(n2 / 2r) = (n2 - 1) / r

now it becomes n2 = 2 (n2-1)

r's cancel out

now it becomes n2 = 2n2 - 2

The answer is n2 = 2

How did they just get 2 when I have n2 = 2n2 - 2

2. Mar 22, 2009

afcwestwarrior

Nevermind I figured it out. It becomes

n2/n2 = ( 2n2/n2) - (2/n2)

then it becomes

1 = 2 - 2/n2

then it becomes

1 + 2/n2 =2

then it becomes

2/n2 = 2 -1

then it becomes

2/n2 = 1

then 2 = n2