(a) (i) Define Optical angle.

(ii) Explain two conditions necessary for total internal reflection to occur. 

(iii) List three practical applications of total internal reflection.

(b) State two effects of refraction. 

(c)(i) Define progressive waves.

(ii) A plane progressive wave is represented by the equation y = 0.5 sin(1000\(\pi\)r = \(\frac{100 \pi \lambda}{17}\)) where y is in millimetres, t in seconds and x in metres.  Calculate the: (\(\alpha\)) frequency of the wave; (\(\beta\))of the wave; (\(\gamma\)) speed of the wave

(a) In an experiment to measure the specific latent heat of vapourisation of water, a student places a heater in a beaker containing water.  The beaker stands on an electronic balance so that the mass of the beaker and water could be measured. The heater is switched on and readings were taken every 100s when the water starts boiling.

The table below shows the readings.

(I) Fill in the mass of water evaporated.

(ii) Given that the heater supplies energy at the rate of 38J/s, fill in the values of the energy supplied by the heater in 100s, 200s, 300s, and 400s. 

(ii) Plot a graph of energy supplied on the vertical axis and mass of water evaporated on the horizontal axis, starting both axes from the origin(0,0). 

(iv) Determine the slope of the graph.

(v) what does the value of the slope mean? 

(a) Define isotopes.

(b) Mention two uses of radioactive tracers in each of the following areas:

(\(\alpha\)) medicine

(\(\beta\)) industry

(\(\gamma\)) agriculture.

(c) State three features of electromagnetic waves.

(d)) Mention four components of the nuclear reactor.

(i) State the functions of each of the components stated in (d)(i).

(a)

You are provided with a metre rule, a knife-edge, set of masses, inextensible string, retort support and other necessary apparatus.

i. Place the metre rule on the knife edge. Read and record the point G where the metre rule balances horizontally, as shown in Fig (a).

ii. Suspend the metre rule at G with the aid of the string provided and attach the string to the retort support as shown in Fig 1(b). Keep the string attached to this point throughout the experiment.

iii. Attach the mass M\(_{0}\) at the 80cm mark of the metre rule. Determine the distance of y from G. Keep M\(_{0}\) at this
position throughout the experiment.

iv. Suspend a mass M= 40g on the side AG and adjust its position until the metre rule balances horizontally.

v. Measure and record the distance of x of M from G. Evaluate x\(^{-1}\)

vi. Repeat the procedure for four other values of M= 60g, 80g, 100g and 120g. Measure and record x and evaluate x\(^{-1}\) in each case.

vii. Tabulate the readings.

viii. Plot a graph of M on the vertical axis and x on the horizontal axis, starting both axes from the origin (0,0).

ix. Determine the slope s of the graph:

x. Given that s = yM\(_{0}\), determine M\(_{0}\).

xi. State two precautions taken to obtain accurate results.

(b) i. Define the moment of a force about a point.

ii. A uniform metre rule is suspended by an inextensible string at its centre of gravity. If a mass of 60g is placed at the 25cm mark, what mass should be placed at the 80cm mark of the metre rule to balance it horizontally?

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\(\frac{\theta}{2}\)

(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.