# Light Ray Path

1. May 17, 2008

### Air

1. The problem statement, all variables and given/known data
The diagrams below illustrate the formation of a rainbow. Figure 1 shows the general arrangement and Figure 2 shows the path of a ray through a raindrop with the centre of the raindrop is labelled O.

Figure 1:

Figure 2:

a.)
Where the ray enters the raindrop in Figure 2, mark the angle of incidence i and the angle of refraction, r.

b.)
Figure 2 is drawn to scale. By taking suitable measurements, show that the refractive index of water is about 1.3.

2. Relevant equations
$\mu = \frac{\sin i}{\sin r}$

3. The attempt at a solution
a.)

^ Have I labelled it correct?

b.)
I measured the angle that I have labelled above and got $i = 25^\circ$ and $r = 35^\circ$ and this gives $\mu = 0.74$. This is incorrect. The correct answer is $i = 53, \ r = 39, \ \implies \mu = 1.27$. Where have I gone wrong here?

2. May 17, 2008

### Redbelly98

Staff Emeritus
The normal should be perpendicular to the water's surface.

3. May 17, 2008

### Air

So, is it like this?

4. May 17, 2008

### Air

Or, is it like this?

5. May 17, 2008

### Nick89

You just seem to be drawing random lines lol...

The normal line on a spherical surface at some point P is always the line that goes from P through the center of the circle.

In other words; if you draw a straight line through the center of a circle, then at the points where it intersects the circle the angle between the line and the circle (at that point) is exactly 90 degrees, or perpendicular.

6. May 17, 2008

### Air

Oooh, I understand now. I guess it is this:

Am I correct?

Last edited: May 17, 2008
7. May 17, 2008

### Redbelly98

Staff Emeritus
Yes, that looks good.