Saved Bookmarks
| 1. |
Derive lens maker's formula for a biconvex lens. |
|
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 refractionat 1st surface of lens an image I. is formed for the object O. If OC = u, CI. = 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 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)))"" ...(ii)`  Adding (i) and (ii), we have `(n_(1))/(v)-(n_(1))/(u)= (n_(2)-n_(1))((1)/(R_(1))-(1)/(R_(2)))` or `(1)/(v)-(1)/(u)=((n_(2))/(n_(1))-1)((1)/(R_(1))-(1)/(R_(2)))` `=(n_(21)-1)((1)/(R_(1))-(1)/(R_(2)))` If `u=oo`, then by definition `v=F` and, hence, `(1)/(f)-(1)/(oo)=(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. |
|