A group of learners investigates how the angle of refraction changes as the angle of incidence is increased for light passing from air into a perspex block....
Question 1 Report
A group of learners investigates how the angle of refraction changes as the angle of incidence is increased for light passing from air into a perspex block. Fig. 5.1 shows the protractor arrangement at the top surface of the block. The normal has been drawn at the point of entry.
Table 5.1 shows the results for six different angles.
| Angle of incidence i / ° | Angle of refraction r / ° | sin i | sin r | sin i / sin r |
|---|---|---|---|---|
| 10 | 7 | 0.174 | 0.122 | |
| 20 | 13 | 0.342 | 0.225 | |
| 30 | 20 | 0.500 | 0.342 | |
| 40 | 26 | 0.643 | 0.438 | |
| 50 | 31 | 0.766 | 0.515 | |
| 60 | 36 | 0.866 | 0.588 |
(a) Record the angle of incidence shown in Fig. 5.1.
angle of incidence = .................. ° [1]
(b) Complete the column for sin i / sin r in Table 5.1. Give your answers to two decimal places. [2]
(c) Calculate the mean value of sin i / sin r. Show your working.
mean = .................. [2]
(d) State the name of the physical quantity represented by the mean value. [1]
(e) State and explain the direction in which the light bends as it enters the perspex from air. [2]
(f) Suggest one source of random error in this experiment. [1]
(g) Describe how the student could reduce the effect of random error on the value of sin i / sin r. [1]
(h) State the independent variable in this experiment. [1]
Answer Details
(a) From the protractor scale on Fig. 5.1, the incident ray makes an angle of approximately 40° with the normal N. [1]
The angle of incidence is read between the incoming ray and the dashed normal line using the protractor markings on the semicircular scale.
(b) Dividing \(\sin i\) by \(\sin r\) for each row:
| i / ° | sin i | sin r | sin i / sin r |
|---|---|---|---|
| 10 | 0.174 | 0.122 | 1.43 |
| 20 | 0.342 | 0.225 | 1.52 |
| 30 | 0.500 | 0.342 | 1.46 |
| 40 | 0.643 | 0.438 | 1.47 |
| 50 | 0.766 | 0.515 | 1.49 |
| 60 | 0.866 | 0.588 | 1.47 |
[1 for correct division method; 1 for at least five values correct to 2 d.p.]
Each ratio is found by dividing the sin i value by the corresponding sin r value. For example, at \(i = 10°\): \(\frac{0.174}{0.122} = 1.43\).
(c) The mean value:
\[ \text{mean} = \frac{1.43 + 1.52 + 1.46 + 1.47 + 1.49 + 1.47}{6} \; [1] \]
\[ = \frac{8.84}{6} = 1.47 \; [1] \]
(d) The mean value of \(\frac{\sin i}{\sin r}\) represents the refractive index of the perspex. [1]
By Snell's law, \(n = \frac{\sin i}{\sin r}\), so this ratio is constant for a given material and equals its refractive index.
(e) As the light enters the perspex from air, it bends towards the normal. [1]
Light passing from a less dense medium (air, \(n \approx 1\)) into a denser medium (perspex, \(n \approx 1.5\)) slows down. The reduction in speed causes the wavefront to change direction, bending the ray towards the normal at the point of incidence. [1]
(f) One source of random error: difficulty reading the protractor to the exact degree, due to the finite thickness of the ray and the precision of the protractor scale. [1]
Other valid sources include parallax when reading angles, slight variation in positioning the ray at the intended angle, or the width of the light beam making the exact centre of the ray ambiguous.
(g) The student should repeat each measurement at least three times at each angle of incidence, calculate the mean value of \(r\) for each \(i\), and then recalculate \(\sin i / \sin r\). Averaging multiple readings reduces the impact of random scatter. [1]
(h) The independent variable is the angle of incidence. [1]
This is the variable the student deliberately changes between trials. The angle of refraction (the dependent variable) is the measured outcome that responds to the change.
Download The App On Google Playstore
Everything you need to excel in your exams
