A convex lens of glass `(mu=1.5)` is formed by combining two surfaces of radii `R_(1)=60 cm` and `R_(2)=30cm` . It is cut into two parts in two different ways as shown in Figure .

Find:
a. the focal length of the lens.
b. in figure (a), the focal length of left portion and that of the right portion.
c. in figure (b), the focal length of the upper part and that of the lower part.

Explanation

a. Using Lensmaker's formuls, we get
`(1)/(f)=(1.5-1) ((1)/(30)-(1)/(-60))=(1)/(2)((1)/(30)+(1)/(60))=(1)/(40)`
`rArrf=+40cm`
b. The focal length of the left position is given by
`(1)/(f_(1))=(1.5-1)((1)/(60)-(1)/(oo))=(1)/(120)`
`rArrf_(1)=+20cm`
and, the focal length of the right portion is give by
`(1)/(f_(1))=(1.5-1)((1)/(oo)-(1)/(-30))=(1)/(60)`
`rArr f_(2)=60cm`
c. Since the refracting surfaces remaing unchanged, therefore the focal lengths of the upper part and the lower part are equal, i.e.,
`f_(1)=f_(2)=+40cm`.