(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.

Question

(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.

Philoid · Accepted Answer

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.