using the diagram above as a guide:
- Trace the outline ABC of the equilateral triangular glass prism provided.
- Remove the prism. Draw a line MN such that it makes an angle i = 5° with the normal at N on side AB of the outline.
- Fix two pins at P\(_{1}\) and P\(_{2}\) on MN. Replace the prism on its outline.
- Looking through the face BC of the prism, fix one pin at P\(_{3}\) and another at P\(_{4}\) Such that they are in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\).
- Remove the prism and the pins. Draw a line to join P\(_{4}\) and P\(_{3}\). Produce line P\(_{4}\)P\(_{3}\) to meet the line BC of the outline at CQ and line MN produced at P.
- Draw a normal to BC at Q. Measure and record the angles \(\theta\) and e. Evaluate \(\phi\) = i + e.
- Repeat the procedure, using a different outline in each case, for four other values of i = 100, 159, 20, and 25 respectively. Evaluate \(\phi\) =i + e in each case. Tabulate your readings.
- Plot a graph of \(\theta\) on the vertical axis against \(\phi\) on the horizontal axis starting both axes from the origin (0,0).
- Determine the slope of the graph and the intercept on the vertical axis.
- State two precautions taken to ensure accurate results.
(b)i. Explain what is meant by the statement: the refractive index of glass is 1.5.
ii. Calculate the critical angle of a medium of refractive index 1.65 when light passes from the medium to air.
Explanation
Table of values / observation
| S/N | L° | e° | \(\theta\)° | \(\theta\) = i + e |
| 1 | 5.0 | 5.0 | 130.0 | 10.0 |
| 2 | 10.0 | 10.0 | 140.0 | 20.0 |
| 3 | 15.0 | 15.0 | 150.0 | 30.0 |
| 4 | 20.0 | 20.0 | 160.0 | 40.0 |
| 5 | 25.0 | 25.0 | 170.0 | 50.0 |
7. Title: The graph of \(\theta\)° vs \(\phi\)
Scale: \(\theta\)° axis: 2cm = 20 units
\(\phi\) axis: = 2cm = 20 units
8. Slope/gradient = \(\frac{\bigtriangleup \theta °}{\bigtriangleup \phi °} = \frac{170-120}{50-0} = \frac{50}{50}\) = 1.0
Intercept on the vertical axis (I) = 120°
9. Precautions are:
- I ensured that the objective pins and the image pins were erect and in a straight line to avoid parallax error.
- I ensured that the optical pins were reasonably separated.
- I ensured that I used a sharp-pointed pencil to obtain neat traces.
- I ensured that I look directly at the protractor scales when taking my readings to avoid parallax error.
(b)i. lt means that the ratio of the speed/wavelength of light in air to glass is 1.5. i.e,
n \(\frac{\text {Speed/wavelength in air}}{\text {speed/wavelength in glass}}\) = \(\frac{3}{2}\) = 1.5 pin
ii. \(_{a}\)n\(_{g}\) = \(\frac{1}{\text {sin c}}\), 1.65 = \(\frac{1}{\text {sin c}}\)
= Sin C = \(\frac{1}{1.65}\) = 0.6060
C = sin\(^{-1}\) (0.6060), C = 37.3°