Use the diagram above as a guide to carry out the following experiment.
- Trace the outline ABCD of the rectangular glass prism on the drawing paper provided.
- Remove the prism. Select a point N on AB such that AN is about one-quarter of AB.
- Draw the normal LNM. Also, draw a line RN to make an angle \(\theta\) = 75° with AB at N.
- Fix two pins at P\(_{1}\) and P\(_{2}\) on line RN. Replace the prism on its outline.
- Fix two other pins at P\(_{3}\) and P\(_{4}\) such that they appear to be in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\) when viewed through the prism from DC.
- (vi) Remove the prism and the pins at P\(_{3}\) and P\(_{4}\). Draw a line to join P\(_{3}\) and P\(_{4}\)
- Produce line P\(_{4}\) P\(_{3}\) to meet the line DC at O. Draw a line to join NO.
- Measure and record the values of MO and NO.
- Evaluate \(\theta\) = \(\frac{MO}{NO}\) and cos \(\theta\).
- Repeat the procedure for four other values of \(\theta\) = 65° 55°, 45°, and 35°. In each case, evaluate \(\theta\) and cos \(\theta\).
- Tabulate your readings.
- Plot a graph with cos \(\theta\) on the vertical axis and \(\theta\) on the horizontal axis.
- Determine the slope, s, of the graph.
- State two precautions taken to ensure accurate results
(b)i. State Snell’s law of refraction.
ii. Calculate the critical angle for the glass prism used in the experiment above if its refractive index is 1.5.
Explanation
Observation/table of values
| S/N | \(\theta\)(0) | Mo(cm) | No(cm) | \(\theta\)=\(\frac{MO}{NO}\) | Cos \(\theta\) |
| 1 | 75.0 | 1.60 | 6.60 | 0.100 | 0.260 |
| 2 | 65.0 | 3.00 | 7.00 | 0.290 | 0.420 |
| 3 | 55.0 | 3.10 | 7.30 | 0.390 | 0.570 |
| 4 | 45.0 | 3.10 | 7.60 | 0.480 | 0.700 |
| 5 | 35.0 | 4.50 | 8.00 | 0.520 | 0.820 |
Slope (s) = \(\frac{\bigtriangleup \text {cos} \theta}{\bigtriangleup \theta} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(\frac{MO}{NO} = \frac{0.77-0.20}{0.50-0.17}\)
\(\frac{0.57}{0.33}\)
Slope (s) = 1.72
Graph cos \(\theta\) against = \(\phi\) = \(\frac{MO}{NO}\)
see the graph above.
PRECAUTIONS; i
- Ensured pins are vertical/ erect.
- Ensured neat traces/sharp pencil (shown on trace)
- Ensured reasonable spacing of pins (about 4cm apart)
- Avoided parallax error in reading protractor/metre rule.
(b)i. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media.
Or \(\frac {\text {Sin i}}{\text {Sin r}}\) = a constant for a given pair of media
Where i = angle of incidence;
r = angle of refraction
ii. n = \(\frac{i}{\text{Sin c}}\)
Sin c = \(\frac{1}{1.5}\) = 0.6667
C = sin\(^{-1}\) 0.6667
C = 41.80°