(a) Draw a ray diagram showing the image formation by a compound microscope.

Hence obtain expression for total magnification when the image is formed at infinity.

(b) Distinguish between myopia and hypermetropia. Show diagrammatically how these defects can be corrected.

OR

State Huygens principle. Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets refracted when it propagates from a rarer to a denser medium. Hence verify Snell’s law of refraction.

(b) When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:

(i) Is the frequency of reflected and reflected light same as the frequency of incident light?

(ii) Does the decrease in speed imply a reduction in the energy carried by light wave?

a) The fig. below shows the formation of image by a compound microscope.
 

If the object AB is very close to the focus of the objective lens of focal length f_o, then magnification M_o by the objective lens is given by, 

b) Difference between myopia and hypermetropia,

A concave lens is used for the correction of myopic eye.

Hypermetropia is corrected using a convex lens.

OR

a) Law of Reflection: Let XY is a reflecting surface at which a wavefront is being incident obliquely. Let v be the speed of the wavefront and at time t = 0, the wavefront touches the surface XY at A. After time t, the point B of wavefront reaches the point B¢ of the surface. According to Huygens principle each point of wavefront acts as a source of secondary waves. When the point A of wavefront strikes the reflecting surface, then due to presence of reflecting surface, it cannot advance further; but the secondary wavelet originating from point A begins to spread in all directions in the first medium with speed v. As the wavefront AB advances further, its points A1, A2, A3… etc. strike the reflecting surface successively and send spherical secondary wavelets in the first medium. 
                             

First of all the secondary wavelet starts from point A and traverses distance AA^’ (= vt) in first medium in time t. In the same time t, the point B of wavefront, after travelling a distance BB’, reaches point B’ (of the surface), from where the secondary wavelet now starts. Now taking A as centre we draw a spherical arc of radius AA’ (= vt) and draw tangent A’B’ on this arc from point B’. As the incident wavefront AB advances, the secondary wavelets starting from points between A and B’, one after the other and will touch A’B’ simultaneously. According to Huygens principle wavefront A’B’ represents the new position of AB, i.e., A’B’ is the reflected wavefront corresponding to incident wavefront AB. 

Now, in right-angled  ABB’ and AA’B’

i.e., incident wavefront AB and reflected wavefront A¢ B¢ make equal angles with the reflecting surface XY. As the rays are always normal to the wavefront, therefore the incident and the reflected rays make equal angles with the normal drawn on the surface XY.

i.e., angle of incidence i = angle of reflection r

This is the second law of reflection.

b)  (i) If the radiation of certain frequency interact with the atoms/molecules of the matter, they start to vibrate with the same frequency under forced oscillations.

Thus, the frequency of the scattered light (under reflection and refraction) equals to the frequency of incident radiation.

(ii) No, energy carried by the wave depends on the amplitude of the wave, but not on the speed of the wave.