You are provided with a glass block, plane mirror, and optical pins. Place the glass block on a drawing sheet and trace its outline ABCD as shown in the dia...
Question 1 Report
You are provided with a glass block, plane mirror, and optical pins.
- Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above.
- Remove the block, measure, and record the width W of the block.
- Draw a normal ON to DC at a point about one-quarter the length of DC.
- Draw a line making an angle \(i = 10^\circ\) with the normal.
- Replace the block on its outline and mount the plane mirror vertically behind the block such that it makes good contact with the face AB.
- Stick two pins \(P_{1}\) and \(P_{2}\) on the line MO.
- Looking through the face CD, stick two other pins \(P_{3}\) and \(P_{4}\) such that they appear to be in a straight line with the images of pins \(P_{1}\) and \(P_{2}\) seen through the block.
- Join \(P_{3}\) and \(P_{4}\) with a straight line and extend it to touch the face CD at O.
- Draw a perpendicular line from the midpoint of OO to meet AB at QD.
- Draw lines OQ, O'Q, and normal O'N' produced.
- Measure and record \(\theta\), e and d.
- Evaluate \(m = \sin e\) and \(n = \cos\left(\frac{\theta}{2}\right)\)
- Repeat the procedure for \(i = 20^\circ\), \(30^\circ\), \(40^\circ\) and \(50^\circ\).
- Tabulate your readings.
- Plot a graph with m on the vertical axis and n on the horizontal axis.
- Determine the slope, s, of the graph and evaluate \(q = 2Ws\).
- State two precautions taken to ensure accurate results. (Attach your traces to your answer booklet.)
(b)i. Explain the term refractive index and give a mathematical expression for it in terms of wavelength.
ii. State the conditions necessary for total internal reflection to occur for a given pair of media.
Answer Details
Refraction through a glass block with a plane mirror on face AB
The block is traced as ABCD, the width is measured as \(W = 5.0\ \text{cm}\). For each angle of incidence the emergent ray is fixed by no-parallax pins \(P_3\) and \(P_4\), and the angles \(\theta\) and \(e\) together with the lateral displacement \(d\) are measured directly from the traces. The full set of readings and the derived quantities \(m = \sin e\) and \(n = \cos\!\left(\dfrac{\theta}{2}\right)\) are tabulated below.
Table of readings
| \(i/^{\circ}\) | \(\theta/^{\circ}\) | \(e/^{\circ}\) | \(d/\text{cm}\) | \(m = \sin e\) | \(n = \cos\left(\frac{\theta}{2}\right)\) |
|---|---|---|---|---|---|
| 10 | 10.4 | 10.0 | 3.00 | 0.174 | 0.996 |
| 20 | 19.0 | 20.4 | 3.90 | 0.349 | 0.986 |
| 30 | 20.0 | 30.0 | 6.00 | 0.500 | 0.985 |
| 40 | 30.0 | 40.0 | 7.00 | 0.643 | 0.966 |
| 50 | 30.0 | 50.0 | 7.50 | 0.766 | 0.966 |
Sample evaluations: for \(i = 30^{\circ}\), \(m = \sin 30.0^{\circ} = 0.500\) and \(n = \cos\!\left(\tfrac{20.0^{\circ}}{2}\right) = \cos 10.0^{\circ} = 0.985\). For \(i = 50^{\circ}\), \(m = \sin 50.0^{\circ} = 0.766\) and \(n = \cos 15.0^{\circ} = 0.966\).
Graph of \(m\) against \(n\)
Slope of the graph
Two points on the line of best fit are \((n_1, m_1) = (0.996,\ 0.174)\) and \((n_2, m_2) = (0.966,\ 0.766)\).
\[ s = \frac{m_2 - m_1}{n_2 - n_1} = \frac{0.766 - 0.174}{0.966 - 0.996} = \frac{0.592}{-0.030} = -19.7 \]The slope is \(s = -19.7\) (magnitude \(19.7\)).
Evaluation of \(q = 2Ws\)
With \(W = 5.0\ \text{cm}\) and \(s = -19.7\):
\[ q = 2Ws = 2 \times 5.0\ \text{cm} \times (-19.7) = -197\ \text{cm} \]Hence \(|q| = 197\ \text{cm}\).
Two precautions
- The optical pins were fixed vertically, well separated, and the outline of the block was traced neatly with a sharp pencil so that the rays could be drawn accurately.
- Parallax error was avoided when reading the protractor and metre rule, and zero error on the metre rule was checked before measuring the width \(W\).
(b)(i) Refractive index
The refractive index is the ratio of the velocity of light in air (vacuum) to the velocity of light in a material medium as light waves pass from air into the medium. In terms of wavelength, since the frequency is unchanged on refraction,
\[ n = \frac{\lambda_{1}}{\lambda_{2}} \]where \(\lambda_{1}\) is the wavelength in air, \(\lambda_{2}\) is the wavelength in the material, and \(n\) is the refractive index of the material.
(b)(ii) Conditions for total internal reflection
- The light must be travelling from a denser medium to a less dense medium.
- The angle of incidence in the denser medium must be greater than the critical angle.
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