State three observable phenomena where a particle behaves like waves. State the scientific principle underlying the operation of fibre optics.

(b) Explain each of the following terms as used in fibre optics: (i) core; (ii) cladding

(a)(i) State Hooke's law. (ii) A spring has a length of 0.20 m when a mass of 0.30 kg hangs on it, and a length of 0.75 nm when a mass of 1.95 kg hangs on it. Calculate the: (i) force constant of the spring; (ii) length of the spring when it is unloaded. [g = 10m/s\(^2\)]

(b)(i) What is diffusion? (ii) State two factors that affect the rate of diffusion of a substance. (iii) State the exact relationship between the rate of diffusion of a gas and its density.
(c) A satellite of mass, m orbits the earth of mass. M with a velocity, v at a distance R from the centre of the earth. Derive the relationship between the period T, of orbit and R.

c(ii)
(a)(i) Define dew point. (ii) Explain why dew forms more quickly on the metal parts than on the rubber parts of a bicycle placed in the open overnight.

(b)(i) Explain the statement. the specific heat capacity of copper is 400 J/kg/K. (ii) Two metals, P and Q are supplied with the same quantity of heat.

If the ratio of the specific heat capacity of P to Q is 3: 1 and their masses are in the ratio I:2 respectively.

calculate the ratio of the temperature rise of P to Q.

(c)(i) Define coefficient of thermal conductivity of a material.

The diagram above c(ii) illustrates a composite bar of iron and copper. The bar is insulated along its sides and it has a diameter of 10 mm. The length and thermal conductivity of the iron are 0.15 m and 40 W/m/K, respectively and those of copper are 0.05 m and 360 W/m/K, respectively. If the free ends of the iron and copper are kept at 100°C and 0°C respectively. calculate the (i) temperature at the interface between the bars; (ii) rate of heat flow along the bar.

(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.