How is the refractive index of water calculated in rainbow formation?

[Air]

Homework Statement

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.

Homework Equations

\mu = \frac{\sin i}{\sin r}

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?

 

[Redbelly98]

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

 

[Air]

So, is it like this?

 

[Air]

Or, is it like this?

 

[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.

 

[Air]

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.

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

Am I correct?

 

[Redbelly98]

Yes, that looks good.