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^\circ 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.
Verified Correct Answer: .
Physical Principles & Numerical Solution
Table of values / observation
S/N
L^\circ
e^\circ
\(\theta\)^\circ
\(\theta\) = 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 \(\theta\)^\circ vs \(\phi\)
Scale: \(\theta\)^\circ axis: 2cm = 20 units
\(\phi\) axis: = 2cm = 20 units
8. Slope/gradient = \(\frac{\bigtriangleup \theta ^\circ}{\bigtriangleup \phi ^\circ} = \frac{170-120}{50-0} = \frac{50}{50}\) = 1.0
Intercept on the vertical axis (I) = 120^\circ
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^\circ
Source: Myschool Past Questions Archive (Record #60077)