You are provided with a glass block, a plane mirror, and optical pins.

1. Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above.
2. Remove the block, measure, and record the width W of the block.
3. Draw a normal ON to DC at a point about one-quarter the length of DC.
4. Draw a line making an angle i = 10° with the normal.
5. 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.
6. Stick two pins P\(_{1}\) and P\(_{2}\) on the line MO.
7. 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.
8. Join P\(_{3}\)  and P\(_{4}\) with a straight line and extend it to touch the face CD at O. 
9. Draw a perpendicular line from the midpoint of OO to meet AB at QD.
10. Draw lines OQ, O'Q, and normal O'N' produced.
11. Measure and record \(\theta\), e and d.
12. Evaluate m = sin e and n = cos(\(\frac{\theta}{2}\))
13. Repeat the procedure for i = 20°, 30°, 40° and 50°.
14. Tabulate your readings.
15. Plot a graph with m on the vertical axis and n on the horizontal axis.
16. Determine the slope, s, of the graph and evaluate q = 2Ws.
17. 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.