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#### Question

(i) Derive the mathematical relation between refractive indices* n*_{1} and *n*_{2} of two radii and radius of curvature *R* for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index *n*_{1} and a real image formed in the denser medium of refractive index *n*_{2}. Hence, derive lens maker's formula.

(ii) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?

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A point object 'O' is kept in a medium of refractive index *n*_{1} in front of a convex spherical surface of radius of curvature *R* which separates the second medium of refractive index *n*_{2} from the first one, as shown in the figure

Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of *n*_{1}, *n*_{2} and *R*.

When the image formed above acts as a virtual object for a concave spherical surface separatig the medium *n*_{2} from *n*_{1} (*n*_{2} > *n*_{1}), draw this ray diagram and write the similar (similar to (a)) relation. Hence obtain the expression for the lens maker's formula.