Index of Refraction

The scenario:

A ray of light strikes the center of the (a) flat surface and (b) curved surface of a semicircular glass medium with the angle of incidences in degrees of 10, 20, 30, 40 and 50.

The angles of refraction for each angle of incidence and for each surface were:

(a) flat surface

Angle of incidence (deg) | Angle of Refraction (deg) | Index of refraction
10                       | 6                         | 1.66
20                       | 12                        | 1.65
30                       | 19                        | 1.54
40                       | 25                        | 1.52
50                       | 30                        | 1.53


(b) curved surface

Angle of incidence (deg) | Angle of Refraction (deg)
10                       | 16
20                       | 31
30                       | 50
40                       | 73
50                       | N/A


I used the formula: index of refraction $=\sin(\theta_{incident}) / \sin(\theta_{refracted})$

Questions:

a). Do I still use the same formula to solve for the index of refraction for the curved surface? Because if I use it, I'll get a different index of refraction.

b). If ever they are really different, why are the calculated indexes of refraction for both media are different for each angle of incidence? Is the difference expected?

Thank you!

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Snell's law still applies to the curved surface, but you have to measure the angles of incidence and refraction relative to the surface where the light hits.

The image is my attempt to show parallel rays of light falling on a curved surface. Even though the rays are parallel, the angle of incidence is different for the two rays because it has to be measured relative to the normal at the point the light strikes the surface. Hence the angle $i$ is not the same as the angle $i'$.

Response to comment:

It has become clear from the comments that the problem is that the value of $n$ depends on whether the light is passing from the air to glass or from glass to air. To be precise the two refractive indices are reciprocals of each other i.e.

$$n_{air-glass} = \frac{1}{n_{glass-air}}$$

The refraction of the light ray happens because the speed of light, and therefore the wavelength, changes when the light enters and leaves the glass. The refractive index when a light ray passes from a medium 1 to a medium 2 is:

$$n_{1-2} = \frac{v_1}{v_2}$$

where $v_1$ is the speed of light in medium 1 and $v_2$ is the speed of light in medium 2. So in our example the refractive index when passing from medium 2 to medium 1 is:

$$n_{2-1} = \frac{v_2}{v_1}$$

i.e.

$$n_{1-2} = \frac{1}{n_{2-1}}$$

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The angles were measured with the use of an optical disk. And the flat surface of the semicircular coincides with the component axis of the disk. And we make sure that the ray strikes the center of the glass for both trials (and surfaces). So, did I get the right angles? And are the indices of refraction really different for each surface? And If ever they aren't, why are they different? –  Cossette Nov 20 '12 at 7:57
The refractive index is a property of the material, so if it's the same lens the refractive index will be the same regardless of which side of the lens the light falls on. If you're getting a different value for $n$ there must be something about the geometry of the experiment. Can you post a diagram or better still a picture of the experimental kit you used. –  John Rennie Nov 20 '12 at 8:38
The set-up somehow look like this. google.com.ph/… –  Cossette Nov 20 '12 at 8:47
Ah, are you shining the light through the curved side and then measuring the refraction when it leaves the glass block at the flat side? In that case the the refractive index you need to use is 1/$n$ i.e. about 0.65. In fact when I calculate $n$ from your data I get 0.65 $\pm$ 0.02 and this is about right. Let me know if you need me to explain this further and I'll edit my answer to go into more detail. –  John Rennie Nov 20 '12 at 9:10
If I try using a different formula for finding the index of refraction for the curved surface : n = sin(refracted angle)/ sin(incident angle). (just the inverse of the formula I used for the flat surface trial) I get indices of refraction almost similar to the indices of refraction I calculated from the flat surface trial. Why is that so? –  Cossette Nov 20 '12 at 9:13