TEST OF PRACTICAL KNOWLEDGE QUESTION Using the diagram above as a guide, carry out the following instructions: Fix. the drawing paper provided on the drawin...

TEST OF PRACTICAL KNOWLEDGE QUESTION

Using the diagram above as a guide, carry out the following instructions:

1. Fix. the drawing paper provided on the drawing board
2. Place the mirror vertically with its longer side resting on the drawing paper. Trace the outline AB of the mirror. Remove the mirror.
3. Draw a normal PQ to meet the outline at the middle Q.
4. Draw a straight line through A to meet the outline of the mirror at the right angle.
5. Trace the incident ray, Q with pins \(P_{1}\) and \(P_{2}\) so that it meets the perpendicular line through A at C such that \(CA=X= 1.0m\).
6. Replace the mirror on its outline. Locate the images of \(P_{1}P_{2}\) through the mirror using two other pins \(P_{3}\) and \(P_{4}\) so that \(P_{3}\) and \(P_{4}\) and the images of \(P_{1}\) and \(P_{2}\) are in a straight line.
7. Remove the mirror and pins \(P_{3}\) and \(P_{4}\).
   Draw a straight line through the pin points to meet AB at Q and CA produced at D.
8. Measure and record angle ACQ as \(è_{1}\), and angle ADCQ as \(è_{2}\). Also, record the value of x. Evaluate \(è = (è_{1} + è_{2})\), \(x^{-1}\) and tan è.
9. Repeat the procedure for four other values of x = 2.0, 3.0, 4.0 and 5.0cm. Tabulate your readings.
10. Plot a graph of tan è on the vertical axis against x on the horizontal axis.
11. Determine the slope, s, of the graph. Evaluate k = 2s
12. State two precautions taken to ensure accurate results. Attach your traces to your answer booklet.

(b)i. Distinguish between regular and diffused reflections.

ii. An object is situated 25cm in front of a plane mirror. Determine the distance of the image from the object. What is the size of the image relative to the object?

(a) Plane-mirror practical

The ray trace obtained is represented below. The angle used is

\[ \theta=\frac{1}{2}(\theta_1+\theta_2). \]

Table of observations

S/N	\(\theta_1\) (°)	\(\theta_2\) (°)	\(x\) (cm)	\(x^{-1}\) (cm\(^{-1}\))	\(\theta\) (°)	\(\tan\theta\)
1	83.0	81.0	1.0	1.00	82.0	7.115
2	76.0	74.0	2.0	0.50	75.0	3.732
3	69.0	70.0	3.0	0.33	69.5	2.675
4	62.0	63.0	4.0	0.25	62.5	1.921
5	57.0	58.0	5.0	0.20	57.5	1.570

Since \(\tan\theta\) is proportional to \(x^{-1}\), the graph of \(\tan\theta\) against \(x^{-1}\) is plotted below.

Using two widely separated points on the line of best fit, \((0.14,\,1.2)\) and \((1.00,\,7.2)\):

\[ s=\frac{\Delta(\tan\theta)}{\Delta(x^{-1})} =\frac{7.2-1.2}{1.00-0.14} =\frac{6.0}{0.86}=6.98\ \text{cm}. \] \[ k=2s=2(6.98)=13.96\ \text{cm}\approx 14.0\ \text{cm}. \]

Precautions:

1. The optical pins were kept vertical and well spaced apart.
2. Parallax was avoided when aligning the image pins with the images of the object pins.

(b)(i)

Regular reflection occurs when parallel rays fall on a smooth surface and are reflected parallel in one direction. Diffused reflection occurs when parallel rays fall on a rough surface and are reflected in different directions.

(b)(ii)

The image is 25 cm behind the mirror while the object is 25 cm in front of it. Hence, the distance between the object and its image is

\[ 25+25=50\ \text{cm}. \]

The image is the same size as the object.

Read lesson note on Electrostatics (JAMB)