Optics Problem: What am I doing wrong?

1. Jan 29, 2005

xenogizmo

Hey Everyone..
I'm having trouble with this question, I think I have this question figured out but my answer is coming out incorrect... Tell me if there is a flaw in my logic.. question is:

"Suppose that a luminous star of radius R1=1.74×108 m is surrounded by a uniform atmosphere extending up to a radius R2=4.28×108 m and with index of refraction n=1.82. When the sphere is viewed from a location far away in vacuum, what is its apparent radius?"

What I did was consider the outer edge of the atmosphere a spherical refracting surface.. and using the equation: n1/P + n2/q = (n2-n1)/R
(sorry for not using latex)

And then I took a point from the star's surface, and take the distance form the atmosphere to that point the image distance (where P is just R2 - R1).
I also took n1 as 1.82 and n2 as 1 since it's just vacuum.. and according to the sign conventions the radius should be negative..

After I got the image distance (which was negative, a virtual image), I subtracted it's absolute value from R2, and that should be apparent radius. Am I wrong?

Thx,
Xeno

2. Jan 29, 2005

xenogizmo

btw, the answer I got when I did this was 2.313x10^8 m

there's a hint on that question but it made sense to me.. Here it is just in case: "What is special about the case R2 > n*R1? "

3. Jan 30, 2005

xenogizmo

Ideas anyone?

4. Jan 30, 2005

5. Feb 1, 2005

ehild

Last edited: Jun 29, 2010
6. Feb 2, 2005

GCT

I found the original problem online and it seems that they wanted the answer in your form, since one had to incorporate the given R2>nR1