Using the diagram as a guide, carry out the following instructions:
- Fix a plain sheet of paper on the drawing board.
- Place the rectangular glass prism on the paper and trace its outline, ABCD. Remove the prism.
- Draw a normal NMP to meet AB and DC at M and P respectively such that |AM| =|DP| = 2.0cm.
- Trace the ray PQ with two pins, P\(_{1}\), and P\(_{2}\), at P and Q respectively such that angle MPQ = i = 5º.
- Replace the prism on its outline. Trace the emergent ray with two other pins P\(_{3}\) and P\(_{4}\) such that they lie in a straight line with P\(_{2}\) and the image of P\(_{1}\) viewed through the glass prism.
- Measure and record \(\theta\), the angle between the emergent ray and the face AB of the glass prism.
- Evaluate cos \(\theta\) and sin i.
- Repeat the procedure for four other values of i= 10°, 15°, 20°, and 25°. Tabulate your readings.
- Plot a graph of cos \(\theta\) on the vertical axis against sin i on the horizontal axis.
- Determine the slope of the graph.
- State two precautions taken to ensure accurate results. Attach your traces to your answer booklet
(b)i. State the laws of refraction of light.
ii. Explain what is meant by the statement the refractive index of a material is 1.65.
Explanation
Table of values
| i° | \(\theta\) | Cos\(\theta\) | Sin i |
| 5° | 81° | 0.156 | 0.087 |
| 10° | 74° | 0.276 | 0.174 |
| 15° | 69° | 0.358 | 0.259 |
| 20° | 61° | 0.484 | 0.342 |
| 25° | 51° | 0.629 | 0.423 |
Slope = \(\frac{x_{2}-x_{1}}{y_{2}-y_{1}}\) = \(\frac{0.6-0.1}{0.4-0.05} = \frac{0.5}{0.35}\) = 1.43
Precautions:
- Avoid error due to parallax
- The direction of the light rays must not be blocked when fixing the search pin or viewing through the glass prism
- The optical pins must be straight and not bend.
(b)i. The first law of refraction of light states that the incident ray, the reflected ray, and the normal ray at the point of incidence all lie in the same plane. The second law of refraction of light states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for the media concerned.
i.e, \(\frac{\text {Sin i}}{\text {Sin r}}\) = a constant
(i1) The statement, "the refractive index of a material is 1.65" means that the ratio of the speed of light in a vacuum to the speed of light in the medium is numerically equal to 1.65.
i.e; Refractive index (n) = \(\frac{\text {speed of light in vacuum}}{\text {speed of light in the medium}}\) = 1.65
The refractive index of any medium depends on the wavelength of the incident light.