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Obtain lens maker's formula using the expression n_(2)/v - n_(1)/u = (n_(2)-n_(1))/R, propagating from a rarer medium of refractive index (n_(1))to a denser medium of refractive index (n_(2)) is incident on the convex side of spherical refracting surface of radius of curvature R. |
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Answer» Solution :Consider a point object O situated on the PRINCIPAL axis of a biconvex lens, whose two surfaces have radii of curvature `R_(1)`and `R_2`, respectively. As SHOWN in figure due to refraction at 1st surface of lens an image Y is formed for the object O. If `OC = u, Cl. =v.` then using the refraction formula at a single spherical surface, we have `n_(2)/v. = n_(1)/u = (n_(2)-n_(1))/R_(1)`.....(i) The image Y BEHAVES as a VIRTUAL object for refraction at the second surface of the lens and the final real image is formed at J. Thus, for second surface applying refraction formula, we have `n_(1)/v - n_(2)/v^(.) = (n_(1)-n_(2))/R_(2) = (n_(2)-n_(1))/(-R_(2))`......(ii)  Adding (i) and (ii), we have `n_(1)/v - n_(1)/u = (n_(2)-n_(1))(1/R_(1) - 1/R_(2))` `=(n_(21) -1)(1/R_(1) -1R_(2))` If `u = infity`, then by the definition v=f and, hence, `1/f -1/infty = (n_(21)-1) (1/R_(1)-1/R_(2)) rArr 1/f = (n_(21)-1) (1/R_(1) - 1/R_(2))` This relation is known as lens maker.s formula. |
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