(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Paralel light rays travel from air to a glass hemisphere with radius R and

index of refraction n[tex]_{g}[/tex]that is greater than n[tex]_{air}[/tex]. A top view is shown in the attached image.

(a) Where do the rays focus relative to the point P?

(b) The index of refraction of the hemisphere is increased by 0.5 percent. Does the

focus point change from that in part (a)? If so, then by how much?

Radius=-R (negative since its concave from the picture)

n[tex]_{air}[/tex]=1.00

2. Relevant equations

[tex]\frac{n1}{s}[/tex] + [tex]\frac{n2}{s'}[/tex] = [tex]\frac{n2-n1}{R}[/tex] where solving for s' would give the point of focus,f (ie. s'=f)

I don't think i can use any of the thin lens eqn's since, well, its not a thin lens right?

3. The attempt at a solution

Here, i'm very confused about what we can assume. Is the distance of the source, s, approximately infinity? or would the source be the distance from p to the flat surface, the radius, R? I'm not really sure either how the rays would interact with the curved surface once it goes through.

If i assume that s=[tex]\infty[/tex], then i get with the above equation to be f=[tex]\frac{-R}{1-n1}[/tex] But how do i justify that assumption?

Also, if I assume s=R, then i get f=-R.

I'm really sure if either of these are correct, and if one is...why exactly is it correct?

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# Ray Optics (Refraction Theory)

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