Using the diagram as a guide, carry out the following instructions: Fix a plain sheet of paper on the drawing board. Place the rectangular glass prism on th...

Answer Details

(a) Refraction through a rectangular glass prism

The outline ABCD of the rectangular glass prism is traced on the paper. The normal NMP is drawn to meet AB at M and DC at P, with \(|AM|=|DP|=2.0\,\text{cm}\). The incident ray PQ is fixed with pins \(P_1\) and \(P_2\) at the chosen angle \(i=\angle MPQ\). With the prism replaced, the emergent ray is traced with pins \(P_3\) and \(P_4\) set in line with \(P_2\) and the image of \(P_1\) seen through the glass. The angle \(\theta\) between the emergent ray and face AB is measured, and \(\cos\theta\) and \(\sin i\) are evaluated. The set-up is shown below.

Table of readings

\(i\,/\,^{\circ}\)	\(\theta\,/\,^{\circ}\)	\(\cos\theta\)	\(\sin i\)
5	81	0.156	0.087
10	74	0.276	0.174
15	69	0.358	0.259
20	61	0.484	0.342
25	51	0.629	0.423

Graph of \(\cos\theta\) against \(\sin i\)

Slope of the graph

The slope is read from two widely separated points on the line of best fit, using the first and last tabulated points \((\sin i,\ \cos\theta)=(0.087,\ 0.156)\) and \((0.423,\ 0.629)\):

\[ \text{slope}=\frac{\Delta(\cos\theta)}{\Delta(\sin i)}=\frac{0.629-0.156}{0.423-0.087}=\frac{0.473}{0.336} \]\[ \boxed{\text{slope}\approx 1.41} \]

Two precautions

1. Parallax error was avoided when reading the angles and when sighting the pins.
2. The optical pins were kept straight (not bent) and fixed vertically, well spaced apart, so that the incident and emergent rays could be aligned accurately.

(b)(i) Laws of refraction of light

1. First law: The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
2. Second law (Snell's law): The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media, \[ \frac{\sin i}{\sin r}=\text{constant}. \]

(b)(ii) Meaning of a refractive index of 1.65

It means that the ratio of the speed of light in a vacuum to the speed of light in the material is equal to 1.65:

\[ n=\frac{\text{speed of light in vacuum}}{\text{speed of light in the material}}=1.65. \]

Equivalently, light travels 1.65 times faster in a vacuum than inside the material, and for a ray passing from air into the material \(\dfrac{\sin i}{\sin r}=1.65\).