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Lens maker's formula is a formula corelating the power P (or focal length f) of a lens to radii of curvature of the two surfaces of the lens and the refractive index of lens material with respect to its surroundings. The formula is expressed as : P=(1)/(f)=(n-1)((1)/(R_(1))-(1)/(R_(2))) where n = refractive index of the material of lens with respect to its surroundings (ordinarily air) and R_(1) and R_(2) are the radii of curvature of two surfaces of the lens. The relation is true under all conditions but while applying it we should put values of P, f, R_(1) and R_(2) with their proper signs as per sign convention being followed by us. Let us have a bi- convex lens and let radii of curvature of both its curved surfaces is same i.e., |R_(1)|=|R_(2)|=R" (say)" Let the given biconvex lens be divided in two equal parts, as shown in Fig. (a), along a section YY' which is perpendicular to the principal axis of lens. What is the power of each part? |
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Answer» Solution :For given biconvex lens `|R_(1)|=|R_(2)|=R` and as per sign CONVENTION `R_(1)` is positive but `R_(2)` is positive but `R_(2)` is NEGATIVE, hence power P of biconvex lens is `P=(n-1)[(1)/((+R))-(1)/((-R))]=(2(n-1))/(R )` When the lens is divided in TWO parts along the SECTION YY., each part behaves as PLANOCONVEX lens for which `R_(1)=R` and `R_(2)=oo`, Hence, power of each part is `P.=(n-1)((1)/(R )-(1)/(oo))=((n-1))/(R )=(P)/(2)` So power of each part is half of that of given biconvex lens. |
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