# Ray Optics (Refraction Theory)

1. Jan 29, 2010

### lmnt

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$$_{g}$$that is greater than n$$_{air}$$. 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$$_{air}$$=1.00

2. Relevant equations

$$\frac{n1}{s}$$ + $$\frac{n2}{s'}$$ = $$\frac{n2-n1}{R}$$ 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=$$\infty$$, then i get with the above equation to be f=$$\frac{-R}{1-n1}$$ 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?

2. Jan 29, 2010

### ideasrule

If the object is at infinity (s=infinity), the image would be at the focal point, so f=-R/(1-n1). If you bring the object closer, the point where the light rays focus would increase, becoming -R at s=R. To calculate the answer for a), you need to know where point P is.

3. Jan 29, 2010

### lmnt

oohhkay thanks for clarifying, and i attached a picture, but i don't really noe where that went...anways, it showed a hemisphere with rays coming at it from the right...like p·( <---
and point · p would be at the centre of the curve. So then, from what you're saying, the focus point would be R away? And another question, if it doesnt indicate a source, it just says parallel light rays are coming towards the glass, then do i consider the source as infinity?