You are provided with a glass block, plane mirror, and optical pins. (i) Place the glass block on a drawing sheet and trace its outline ABCD as shown in the...
You are provided with a glass block, plane mirror, and optical pins.
(i) Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above.
(ii) Remove the block, measure and record the width W of the block.
(iii) Draw a normal ON to DC at a point about one-quarter the length of DC.
(iv) Draw a line making an angle \(i = 10°\) with the normal.
(v) 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.
(vi) Stick two pins \(P_{1}\) and \(P_{2}\) on the line MO.
(vii) 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.
(viii) Join \(P_{3}\) and \(P_{4}\) with a straight line and extend it to touch the face CD at \(O^{1}\).
(ix)Draw a perpendicular line from the midpoint of \(OO^{1}\) to meet AB at Q.
(x) Draw lines OQ, \(O^{1}\)Q and normal \(O^{1}N^{1}\) produced.
(xi) Measure and record \(\cos\theta\), e, and d.
(xii) Evaluate \(m = \sin e\), and \(n \cos\left(\frac{\theta}{2}\right)\)
(xii)Repeat the procedure for \(i = 20°\), \(30°\), \(40°\) and 50.
(xiv) Tabulate your readings.
(xv) Plot a graph with m on the vertical axis and n on the horizontal axis.
(xvi) Determine the slope, s, of the graph and evaluate \(\cos\theta = 2Ws\).
(xvii) State two precautions are taken to ensure accurate results.
(xviii) Sketch a diagram to show the path of the ray through the glass block when the angle of incidence \(i = 90°\) in the experiment above.
(xix) A coin lies at the bottom of a tank containing water to a depth of 130cm. If the refractive index of water is 1.3, calculate the apparent displacement of the coin when viewed vertically from above.
(a) Refraction through a glass block with a plane mirror
The outline ABCD of the glass block is traced and the block is removed. The width of the block is measured as \(W = 6.5\,\text{cm}\). A normal ON is drawn to face DC and an incident ray MO is set at angle \(i\) to the normal. With the block replaced and a plane mirror mounted against face AB, pins \(P_1,P_2\) are placed on MO; viewing through face CD, pins \(P_3,P_4\) are lined up with the images of \(P_1,P_2\). The emergent line \(P_3P_4\) is produced to CD at \(O^{1}\), the perpendicular from the midpoint of \(OO^{1}\) meets AB at Q, and the angles \(\theta\) and \(e\) and the displacement \(d\) are read for each incidence. For each value of \(i\) we evaluate \(m=\sin e\) and \(n=\cos(\theta/2)\).
Table of readings
\(i/^{\circ}\)
\(\theta/^{\circ}\)
\(e/^{\circ}\)
\(d/\text{cm}\)
\(m=\sin e\)
\(n=\cos(\theta/2)\)
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
30.5
50.0
7.50
0.766
0.965
Graph of \(m\) against \(n\)
\(m=\sin e\) is plotted on the vertical axis against \(n=\cos(\theta/2)\) on the horizontal axis:
Line of best fit; slope s = (0.766 - 0.174)/(0.965 - 0.996) = -19.1
Slope of the graph
Taking two well-separated points on the line of best fit, \((n_1,m_1)=(0.996,\,0.174)\) and \((n_2,m_2)=(0.965,\,0.766)\):
The outline of the block was traced neatly with a sharp pencil.
The pins were fixed truly vertical.
The pins were spaced reasonably far apart to improve alignment.
Parallax error was avoided while reading the protractor and ruler.
Zero error was avoided on the metre rule.
(b) Refractive index and total internal reflection
(i) The refractive index of a medium is the ratio of the velocity of light in air (vacuum) to the velocity of light in the medium as light passes from air into the material medium. In terms of wavelength:
\[ n=\frac{\lambda_{1}}{\lambda_{2}} \]
where \(\lambda_{1}\) is the wavelength of the light in air, \(\lambda_{2}\) is the wavelength of the light in the material, and \(n\) is the refractive index of the material.
(ii) Two conditions necessary for total internal reflection to occur:
The light must be travelling from a denser (optically denser) medium to a less dense medium.
The angle of incidence in the denser medium must be greater than the critical angle for the two media.
(a) Refraction through a glass block with a plane mirror
The outline ABCD of the glass block is traced and the block is removed. The width of the block is measured as \(W = 6.5\,\text{cm}\). A normal ON is drawn to face DC and an incident ray MO is set at angle \(i\) to the normal. With the block replaced and a plane mirror mounted against face AB, pins \(P_1,P_2\) are placed on MO; viewing through face CD, pins \(P_3,P_4\) are lined up with the images of \(P_1,P_2\). The emergent line \(P_3P_4\) is produced to CD at \(O^{1}\), the perpendicular from the midpoint of \(OO^{1}\) meets AB at Q, and the angles \(\theta\) and \(e\) and the displacement \(d\) are read for each incidence. For each value of \(i\) we evaluate \(m=\sin e\) and \(n=\cos(\theta/2)\).
Table of readings
\(i/^{\circ}\)
\(\theta/^{\circ}\)
\(e/^{\circ}\)
\(d/\text{cm}\)
\(m=\sin e\)
\(n=\cos(\theta/2)\)
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
30.5
50.0
7.50
0.766
0.965
Graph of \(m\) against \(n\)
\(m=\sin e\) is plotted on the vertical axis against \(n=\cos(\theta/2)\) on the horizontal axis:
Line of best fit; slope s = (0.766 - 0.174)/(0.965 - 0.996) = -19.1
Slope of the graph
Taking two well-separated points on the line of best fit, \((n_1,m_1)=(0.996,\,0.174)\) and \((n_2,m_2)=(0.965,\,0.766)\):
The outline of the block was traced neatly with a sharp pencil.
The pins were fixed truly vertical.
The pins were spaced reasonably far apart to improve alignment.
Parallax error was avoided while reading the protractor and ruler.
Zero error was avoided on the metre rule.
(b) Refractive index and total internal reflection
(i) The refractive index of a medium is the ratio of the velocity of light in air (vacuum) to the velocity of light in the medium as light passes from air into the material medium. In terms of wavelength:
\[ n=\frac{\lambda_{1}}{\lambda_{2}} \]
where \(\lambda_{1}\) is the wavelength of the light in air, \(\lambda_{2}\) is the wavelength of the light in the material, and \(n\) is the refractive index of the material.
(ii) Two conditions necessary for total internal reflection to occur:
The light must be travelling from a denser (optically denser) medium to a less dense medium.
The angle of incidence in the denser medium must be greater than the critical angle for the two media.
