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Using lens maker's formula, derive the thin less formula 1/f=1/v-1/u for a biconevex lens. |
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Answer» Solution :Consider a point object O situated on the principal axis of a bloonvex 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!. is formed for the object of 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))` The image I. behaves as a virtual object for refraction at the second surface of the lens and the final real image is formed at I. 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))` Addng (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)-1/R_(2))` However, we know that as per lens maker.s formula `1/f=(n_(21)-1) (1/R_(1)-1/R_(2))` Comparing (iii) and (iv), we get the thin lens formula `1/f=1/v-1/u` |
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