(a) (i) Draw a ray diagram to show the working of a compound microscope. Obtain the expression for the total magnification for the final image to be formed at the near point.

(ii) In a compound microscope an object is placed at a distance of $$1.5 \mathrm{~cm}$$ from the objective of focal length $$1.25 \mathrm{~cm}$$. If the eye-piece has a focal length of $$5 \mathrm{~cm}$$ and the final image is formed at the near point, find the magnifying power of the microscope.

OR

(b) (i) Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.

(ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of $$150 \mathrm{~cm}$$. Find the focal lengths of the two lenses.