Q26 of 26 Page 1

(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.

(b) Obtain the mirror formula and write the expression for the linear magnification.


(c) Explain two advantages of a reflecting telescope over a refracting telescope.


OR


(a) Define a wave front. Using Huygens’ principle, verify the laws of reflection at a plane surface.


(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band ? Explain.


(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle. Explain why.

a)



b)



From the figure given above, we can see that the two right angled triangles A’B’F and MPF are similar. For paraxial rays, MP can be considered to be a straight line perpendicular to CP. Therefore,




Since ∠ APB = ∠ A’PB’, the right-angled triangles A’B’P and ABP are also similar. Therefore,



Comparing equations (i) and (ii), we get



The light travels from the object to the mirror MPN. Hence this is taken as the positive direction. To reach the object AB, image A’B’ as well as the focus F from the pole P, we have to travel opposite to the direction of incident light. Hence, all the three will have negative signs. Thus,


B’P = -v , FP = -f ,BP = -u


Using these in equation (iii), we get





This relation is known as mirror equation where v = image distance, u = object distance and f = focal length.


Linear magnification m for mirror is given as



Where h’ = image height


h = object height


c) Advantages of reflecting telescope over refracting telescope are:


1. In reflecting type telescope there is no chromatic aberration as the objective is a mirror.


2. Image is brighter compared to the one formed in refracting type telescope.


OR


a) Wave front: A locus of the points which oscillate in the same phase is called a wavefront. Thus, a wavefront is defined as a surface of constant phase.



Let speed of the wave in the medium be ‘v’


Let the time taken by the wave front, to advance from point B to point C is τ


Hence BC = vτ Let CE represent the reflected wave front


Distance AE = vτ = BC


Δ AEC and Δ ABC are congruent ∴ ∠ BAC = ∠ ECA


⇒∠ i = ∠ r.


b) The size of the central maxima is given as



Where λ = wavelength of light


D = distance between slit and screen


d = width of slit


if d⇒2d then β ⇒β/2.


∴ Size of central maxima reduces to half.


Intensity will increase. This is because the amount of light, entering the slit, has increased and the area, over which it falls, decreases.


c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle because of diffraction and central maxima is always bright.


More from this chapter

All 26 →
22

(a) Give three reasons why modulation of a message signal is necessary for long distance transmission.

(b) Show graphically an audio signal, a carrier wave and an amplitude modulated wave.

 23

The teachers of Geeta’s school took the students on a study trip to a power generating station, located nearly 200 km away from the city. The teacher explained that electrical energy is transmitted over such a long distance to their city, in the form of alternating current (ac) raised to a high voltage. At the receiving end in the city, the voltage is reduced to operate the devices. As a result, the power loss is reduced. Geeta listened to the teacher and asked questions about how the ac is converted to a higher or lower voltage.

(a) Name the device used to change the alternating voltage to a higher or lower value. State one cause for power dissipation in this device.


(b) Explain with an example, how power loss is reduced if the energy is transmitted over long distances as an alternating current rather than a direct current.


(c) Write two values each shown by the teachers and Geeta.

 24

(a) Define electric flux. Is it a scalar or a vector quantity ?

A point charge q is at a distance of d/2 directly above the centre of a square of side d, as shown in the figure. Use Gauss’ law to obtain the expression for the electric flux through the square.



(b) If the point charge is now moved to a distance ‘d’ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.


OR


(a) Use Gauss’ law to derive the expression for the electric field (E) due to a straight uniformly charged infinite line of charge density λ C/m.


(b) Draw a graph to show the variation of E with perpendicular distance r from the line of charge.


(c) Find the work done in bringing a charge q from perpendicular distance r1 to r2 (r2 > r1).

 25

(a) State the principle of an ac generator and explain its working with the help of a labelled diagram. Obtain the expression for the emf induced in a coil having N turns each of cross-sectional area A, rotating with a constant angular speed ω in a magnetic field B directed perpendicular to the axis of rotation.

(b) An aeroplane is flying horizontally from west to east with a velocity of 900 km/hour. Calculate the potential difference developed between the ends of its wings having a span of 20 m. The horizontal component of the Earth’s magnetic field is 5 × 10–4 T and the angle of dip is 30° .


OR


A device X is connected across an ac source of voltage V = V0 sin ωt. The current through X is given as



(a) Identify the device X and write the expression for its reactance.


(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.


(c) How does the reactance of the device X vary with frequency of the ac ? Show this variation graphically.


(d) Draw the phasor diagram for the device X.