(a)(i) Define each of the following terms as it relates to converging lenses (i) focal length; (ii) optical Centre.

(iii) Draw a ray diagram to illustrate how a converging lens is used to produce a virtual image of an object.

(b)(i) Name the primary colors of light. (ii) Match each primary color to its corresponding complementary color.

(c) A ray passes symmetrically through a glass prism of angle 60° and refractive index of 1.5. Calculate the angle of: (i) incidence; (ii) minimum deviation.

(a)(i) What is meant by the root-mean-square value of an alternating current? (ii) Define impedance of an alternating current circuit.

(b) An electrical device rated 120 V, 60 W is opened on a 240 V, 50Hz mains supply. The circuit has a capacitor connected in series with ihe electrical device and the supply. Calculate the capacitance of the capacitor. [π=3.142].

(c)(i) Define the capacitance of a capacitor.

(ii)

The circuit diagram above illustrates two capacitors of capacitance C\(_1\) and C\(_2\) connected in series across a 2V source.

(i)Obtain an expression for the total capacitance in terms of C\(_2\). 2 mm 5 n (ii) Calculate the potential difference across each capacitor.

(a)(i) State the principal factor that determines the relative stability of a radioactive nucleus.

(ii) Arrange the following radioactive nucleus in decreasing order of stability. Justify your answer: X,W and Y: 

\(^40{X}_20\)   \(^920{Y}_36\) and \(^95{Z}_42\)

(b)(i) Explain the term ionization potential.
(ii)

The diagram above illustrates energy levels  in the hydrogen atom. E, is the energy of the E\(_0\) ground state.

(i) When an electron makes a transition from level n = 3 to level n = 1, it emits a photon of wavelength 1.02x 10\(^{-7}\)m. Calculate E\(_0\).

(ii) Calculate the ionization potential of the hydrogen atom.

(c)(i) Explain the statement, the work function of sodium is 2.0 eV. (ii) Light of wavelength 160 mm is shone on the surface of a sodium metal of work function 2.0 eV. Determine whether photoelectrons will be emitted. [h = 6.6 x 10\(^{-34}\) Js, e = 3.0 x 10\(^{8}\)m/s, I eV = 1.6 x 10\(^{-19}\) J]

(a) You are provided with a set of masses, a metre rule, a thread, two retort stands and clamps, a stop watch, a knife edge and split corks.

Carry out the following instructions using the diagram above as a guide.

(i) Determine the centre of gravity, C, of the metre rule using the knife edge.

(ii) Read and record the mass, M, of the metre rule written on the reverse side of it.

(iii) Suspend the metre rule by means of two parallel threads of equal length, h= 70 cm with one at the 10 cm mark and the other at 90 cm mark of the metre rule.

(iv) Attach a mass m = 30g firmly to the metre rule at C. Ensure that the graduated face of the metre rule is facing upwards and that d= 80 cm throughout the experiment. (v) Set the metre rule into small angular oscillations about the vertical axis through its centre of gravity by displacing its ends in opposite directions.

(VI) Determine the time,i, for 20 oscillations and evaluate the period T, T\(^2\) and T\(^{-2}\).

(vii) Repeat the procedure for four other values of m =40 g, 50 g, 60 g and 70 g n each case, determine I and evaluate T\(^2\) and T\(^{-2}\).

(viii) Plot a graph of T on the vertical axis and m on the horizontal axis.

(ix) Determine the slope, s, of the graph.

(x) Evaluate Q= 0.68 / s.

(xi) State two precautions taken to ensure accurate results.

(b) (i) Give two examples of simple harmonic motion other than the motion of a simple pendulum.

(ii) Explain the term centre of gravity of a body.

You have been provided with a ray box, a converging lens, a lens holder, a screen, a metre rule, and half- metre rule. Use the diagram above as a guide to perform the experiment.

(i) Determine the approximate focal length f, of the lens by focusing a distant object on the screen.

(ii) Place the ray box and the screen such that the distance between the illuminated cross-Wire and the screen, D= 150 cm.

(iii) Place the lens at a position L where a sharp mage of the cross-Wire Is obtained on the screen Note L.

(iv) Move the lens at a position L, to 0btain another sharp image of the cross-wire on the screen. Note L

(V) Measure the distance, d. between L\(_1\) and L\(_2\).

(Vi) Evaluate D\(^2\): d\(^2\) and D\(^2\) - d\(^2\).

(vii) Repeat the procedure for four other values of D = 130cm, 100 cm, 90 cm and 80 cm. in each case.evaluate D\(^2\); d\(^2\) and D\(^2\) - d\(^2\).

(viii) Tabulate the result

(ix) Plot a graph with D\(^2\) - d\(^2\) on the vertical axis and  D on the horizontal axis.

(x) Determine the r values of D axis and  Determine the slopes, S, of the graph.

(xi) Evaluate k = \(\frac{s}{4}\)

(xii) State two precautions taken to ensure accurate results.

(bi) Distinguish between a virtual image and. plain image?

(ii) With the aid of a ray diagram, explain how a converging lens produces a Virtual image