You have been provided with a rectangular glass prism, optical pins, and other necessary apparatus. Using the above diagram as a guide, carry out the following instructions:
- Fix the drawing paper provided to the drawing board
- Place the glass prism on the drawing paper and trace the outline, ABCD of the prism
- Remove the prism, mark a point O on AB such that AO is about one-quarter of AB
- Draw a normal through point O. Also draw an incident ray to make an angle i = 25 with the normal at O. Fix two pins at P\(_{1}\) and P\(_{2}\) On the incident ray.
- Replace the prism. Fix two other pins at P\(_{3}\) and P\(_{4}\) such that the pins appear to be in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\) when viewed through the block along DC
- remove the prism. Join points Pa and P4 and produce it to meet DC at 1. Also, draw a line to join Ol (
- With O as center and using any Concinient radius, draw a circle to Cut the incident ray and the refracted ray at E and H respectively. Maintain this radius throughout the experiment
- Draw the perpendiculars EF and GH. Measure and record d= EF and I= GH.
- Repeat the procedure for four other values of i = 35°, 45, 55°, and 65° respectively. In each case measure and record d and I
- Plot a graph of d on the vertical axis against 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 Snell’s law.
ii. Calculate the critical angle for a water-air interface. [refractive index of water = \(\frac{4}{3}\)]
Explanation
Table of values (Observation)
| S/N | iº | d(cm) | i (cm) |
| 1 | 25° | 0.85 | 0.55 |
| 2 | 35° | 1.15 | 0.75 |
| 3 | 45° | 1.50 | 0.95 |
| 4 | 55° | 1.65 | 1.10 |
| 5 | 65° | 1.85 | 1.20 |
Slope of the graph = \(\frac{y}{x} = \frac{\bigtriangleup {d}}{\bigtriangleup {L}} = \frac{1.4}{0.9}\) = 1.56
Precautions:
- I ensured that pins were vertical.
- l ensured that pins were reasonably spaced (at least 1 cm apart) and pinpoints were seen on traces.
- I ensured neat traces (sharp pencils)
- I noted and corrected zero errors on the metre rule.
- l avoided parallax using metre rule/protractor
(b) Snell's law states that for a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant. Or 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. Or
\(\frac{\text {sin i}}{\text {sin r}}\) = a constant for a given pair of media where
i = angle of incidence and
r = angle of refractions.
ii. \(\frac{1}{\text { sin C}}\) = \(_{a}\)n\(_{w}\)
Where C = critical angle, and
\(_{a}\)n\(_{w}\) = refractive index of water.
i.e. sin C = \(\frac{3}{4}\) = 0.75
C = sin\(^{-1}\), 0.75 = 48.6°