# Find the formula for refraction angle?

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1. Jun 14, 2017

### Helly123

1. The problem statement, all variables and given/known data

2. Relevant equations
Snell's Law
sin tetha1/v1 = sin tetha2/v2
n1 = c/v1
n1 . sin tetha 1 = n2 . sin tetha 2

3. The attempt at a solution
I try to make triangle out of line PO, so that it will have correlation to tetha, since o = center, then let's say there's point C at circle circumference. then POC is isosceles triangle.
PC^2 = PO^2 + CO^2 - 2PO.CO.cos tetha
PC^2 = 2R^2 - 2R^2 cos tetha
PC^2 = 2R^2 ( 1 - cos tetha)
n value for air = 1.00 ? but I cannot find the correlation tetha to n, and especially h...?

2. Jun 14, 2017

### Staff: Mentor

Extend the line OP. That gives you the normal to the surface. The angle of incidence can be related to h & r with a bit of trig.

3. Jun 14, 2017

### Helly123

i tried to extend OP but still don't find the correlation with r and h

4. Jun 15, 2017

### Helly123

5. Jun 15, 2017

### haruspex

Q is the point where the vertical marked h meets the horizontal through O.
S is thepoint at the top of the line marked h.
R is a point beyond P on the line through OP.
Can you relate angle POQ to h and r?
Can you relate angle POQ to angle RPS?
Can you relate angle RPS to φ?

6. Jun 15, 2017

### Helly123

I tried before, is it right?
i'm not sure about the normal line I set, and theory I used

7. Jun 15, 2017

### Staff: Mentor

Now you're cooking. Looks perfect!