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° 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(\(\frac{\theta}{2}\))
- Repeat the procedure for i = 20°, 30°, 40° and 50°.
- 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.
Explanation
| i/° | \(\theta\)/° | e/° | d/cm | m = sine/° | n = cos[\(\frac{\theta}{2}\)]/° |
| 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 | 0.965 |
Slope = \(\frac{0.766-0.174}{0.965-0.996} = \frac{0.592}{-0.031}\) = -19.097°
q = 2Ws
Precautions;
- Neat traces
- Pins located vertically, Pins reasonably spaced
- Avoided parallax error while reading the protractor/ ruler
- zero error was avoided on the metre rule.
(b) Refractive index is the ratio of the velocity of light in air to the velocity of light in a medium when light waves pass from air to a material medium.
Mathematically,
n =\(\frac{\lambda_{1}}{\lambda_{2}}\). Where,
\(\lambda_{1}\) = wavelength in air
\(\lambda_{2}\) = wavelength in material
n = refractive index of the material.
ii. The light must be traveling from a denser medium to a less dense medium. The angle of incidence in the denser medium must be greater than the critical angle.