(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.

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between $$u, v$$ and $$f$$ for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

(i) An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image? If not, explain.

(ii) A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed? Explain.

(iii) A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is $$20 \mathrm{~cm}$$.

OR

(iii) Two convex lenses A and B of focal lengths $$15 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively are placed coaxially '$$d$$' distance apart. A point object is kept at a distance of $$30 \mathrm{~cm}$$ in front of lens A. Find the value of '$$d$$' so that the rays emerging from lens $B$ are parallel to its principal axis.

A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain desired value of capacitance.

(i) Find the equivalent capacitance between points A and B in the given diagram.

(ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases. Explain.

(iii) A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance $$2 C$$. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.

OR

(iii) Two slabs of dielectric constants $$2 \mathrm{~K}$$ and $$\mathrm{K}$$ fill the space between the plates of a parallel plate capacitor of plate area A and plate separation $$d$$ as shown in figure. Find an expression for capacitance of the system.