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Derive the mathematical relation between refractive indices n_(1)and n_2 of two media and radius of curvature R for refraction at a convex spherical surface. Consider the object to be a point one lying on the principal axis in rarer medium of refractive index nt 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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Answer» Solution :(i)For relation `n_(2)/v -n_(1)/u =(n_(2)-n_(1))/R`, (ii)It is given here that `u= -100 cm, R = + 20 cm, n_(1) = 1` (for air) and `n_2 = 1.5` (for GLASS). We KNOW that for refraction through a spherical surface `n_(2)/v -n_(1)/u =(n_(2)-n_(1))/R` `therefore 1.5/v -1/(-100) = (1.5-1)/20` or `1.5/v = 0.5/20 -1/100 = 1.5/100 rArr v= 100 cm` |
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