TEST OF PRACTICAL KNOWLEDGE QUESTION
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) Glass block and mirror ray-tracing experiment. The outline ABCD of the block is traced and its width W measured. A normal ON is drawn on face DC, and an incident ray MO is drawn at angle i to the normal. With the block replaced and a plane mirror set against face AB, pins \(P_1,P_2\) are placed on MO and, 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 back to CD, the geometry is completed, and for each incidence the quantities e (emergent-side angle) and \(\theta\) are measured. For each i, evaluate \(m=\sin e\) and \(n=\cos(\theta/2)\), tabulate, and plot m against n. The slope s is measured and \(\cos\theta\) related through \(\cos\theta=2Ws\). When \(i=90^{\circ}\) the ray enters grazing the surface and is refracted at the critical angle.
Two precautions: use sharp, vertical pins spaced well apart for accurate alignment; mark the outline with a sharp pencil and avoid parallax when reading angles.
(xix) Apparent displacement of the coin. Real depth = 130 cm, refractive index n = 1.3.
Apparent depth \(=\dfrac{\text{real depth}}{n}=\dfrac{130}{1.3}=100\,\text{cm}\).
Apparent displacement \(=\text{real depth}-\text{apparent depth}=130-100=30\,\text{cm}\).
The coin appears raised (displaced upward) by 30 cm.
(a) Glass block and mirror ray-tracing experiment. The outline ABCD of the block is traced and its width W measured. A normal ON is drawn on face DC, and an incident ray MO is drawn at angle i to the normal. With the block replaced and a plane mirror set against face AB, pins \(P_1,P_2\) are placed on MO and, 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 back to CD, the geometry is completed, and for each incidence the quantities e (emergent-side angle) and \(\theta\) are measured. For each i, evaluate \(m=\sin e\) and \(n=\cos(\theta/2)\), tabulate, and plot m against n. The slope s is measured and \(\cos\theta\) related through \(\cos\theta=2Ws\). When \(i=90^{\circ}\) the ray enters grazing the surface and is refracted at the critical angle.
Two precautions: use sharp, vertical pins spaced well apart for accurate alignment; mark the outline with a sharp pencil and avoid parallax when reading angles.
(xix) Apparent displacement of the coin. Real depth = 130 cm, refractive index n = 1.3.
Apparent depth \(=\dfrac{\text{real depth}}{n}=\dfrac{130}{1.3}=100\,\text{cm}\).
Apparent displacement \(=\text{real depth}-\text{apparent depth}=130-100=30\,\text{cm}\).
The coin appears raised (displaced upward) by 30 cm.
