(a) State two factors which affect the angle of deviation of a ray of light through a triangular glass prism. (b) Seven virtual images of an object are form...
Question 1 Report
(a) State two factors which affect the angle of deviation of a ray of light through a triangular glass prism.
(b) Seven virtual images of an object are formed when two plane mirrors are inclined at an angle 0 to each other. Calculate the value of 0.
(c) By means of a ripple tank, a student was able to generate series of transverse waves by varying the frequency of the dipper and all the waves so generated covered a distance of 0.80 m in 0.2s.
(i) Determine the speed, v, of the waves.
Copy and complete the table given in your answer booklet.
(iii) Plot a graph with f on the vertical axis and \(\lambda ^{-1}\) on the horizontal axis.
(iv) What does the slope of the graph represent?
Answer Details
(a) Two factors which affect the angle of deviation of a ray through a triangular glass prism:
- The angle of incidence of the ray on the first refracting face.
- The refracting (apex) angle of the prism together with the refractive index of the glass (which itself depends on the colour/wavelength of the light).
(b) Angle between the two plane mirrors.
The number of images formed by two plane mirrors inclined at an angle \(\theta\) is
\[N=\frac{360^\circ}{\theta}-1.\]With \(N=7\):
\[7=\frac{360^\circ}{\theta}-1 \;\Rightarrow\; \frac{360^\circ}{\theta}=8 \;\Rightarrow\; \theta=\frac{360^\circ}{8}=45^\circ.\](c)(i) Speed of the waves.
\[v=\frac{\text{distance}}{\text{time}}=\frac{0.80\ \text{m}}{0.2\ \text{s}}=4.0\ \text{m s}^{-1}.\](ii) Completed table. Using \(\lambda=\dfrac{v}{f}=\dfrac{4.0}{f}\) and \(\lambda^{-1}=\dfrac{1}{\lambda}\):
| \(f\) /Hz | \(\lambda\) /m | \(\lambda^{-1}\) /m\(^{-1}\) |
|---|---|---|
| 2.0 | 2.00 | 0.50 |
| 4.0 | 1.00 | 1.00 |
| 6.0 | 0.67 | 1.50 |
| 8.0 | 0.50 | 2.00 |
| 10.0 | 0.40 | 2.50 |
(iii) Graph of \(f\) (vertical axis) against \(\lambda^{-1}\) (horizontal axis).
The points \((0.50,2.0),(1.00,4.0),(1.50,6.0),(2.00,8.0),(2.50,10.0)\) lie on a straight line passing through the origin, since \(f=v\,(\lambda^{-1})\).
(iv) Meaning of the slope.
Reading two points on the line of best fit, e.g. \((2.50,10.0)\) and \((0.50,2.0)\):
\[\text{slope}=\frac{f}{\lambda^{-1}}=\frac{10.0-2.0}{2.50-0.50}=\frac{8.0}{2.0}=4.0.\]Since \(f=v\times\lambda^{-1}\), the slope \(=f\lambda=v=4.0\ \text{m s}^{-1}\). The slope of the graph represents the speed (velocity) of the waves.
Download The App On Google Playstore
Everything you need to excel in your exams
