(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.

(a) The magnification produced by the compound microscope is the product of the magnifications produced by the eyepieces and objective.
∴M=Me×M0. (i)
Where, Me and M0 are the magnification powers of the eyepiece and objective respectively.
If u0 is the distance of the object from the objective and v0 is the distance of the image from the objective, then the magnifying power of the objective is
M0=h′h=L/f0(Using, tanβ=(h/u0)=(h′/L))
Where h, h' are object and image heights respectively and f0 is the focal length of the objective. L is the tube length i.e the distance between the second focal point of the objective and the first focal point of the eyepiece.
When the final image is at infinity
Me=D/f0
magnifying power of compound microscope.
M=M0×Me=L/f0×D/f0
(b)(i) Nearsightedness or Myopia -A person suffering from myopia can see only nearer objects clearly, but cannot see the objects beyond a certain distance clearly,
Myopia eye:
Correction -To correct the eye for this defect, a concave lens of appropriate focal length is positioned close to the eye so that the parallel ray of light from an object at infinity after refraction through the lens appears to come from the far point P' of the myopia eye
(ii) Farsightedness or Hypermetropia- A person suffering from hypermetropia can see distant objects clearly, but cannot see nearer objects
Hypermetropia eye:
Correction-To correct this defect, a convex lens of suitable focal length is positioned close to the eye so that the rays of light from an object placed at the point N after reflection through the lens appear to come from the near point 'N' of the hypermetropic eye