There are two spherical surfaces of radii `R_(1)=30cm` and `R_(2)=60cm`. In how many ways these surfaces may be arranged to get different lenses. If all the lenses are made of glass `(mu=1.5)` , find the focal length of each lens.

Explanation

Two surfaces may be arranged in four different ways. Using lensmaker's formuls, we can obtain the focal length of each lens as
`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
a. `mu=1.5, R_(1)=+30CM, R_(2)=-60cm`
`:. (1)/(f_(1))=(1.5-1)((1)/(30)-(1)/(60))=(1)/(40)`
`rArr f_(1)=40cm` (converging)
b. `mu=1.5, R_(1)=+30cm, R_(2)=+60cm`
`:. (1)/(f_(2))=(1.5-1)((1)/(30)-(1)/(60))=(1)/(120)`
`rArrf_(2)=+120cm(conver i ng)`
c. `mu=1.5, R_(1)=-30cm, R_(2)=+60cm`
`:. 1/f_(3)=(1.5-1) (1/(-30)-1/60)=(-1)/4`
`rArrf_(3)=-40cm` (diverging)
d. `mu=1.5, R_(1)=-30cm, R_(2)=-60cm`
`:. (1)/(f_(4))=(1.5-1)((1)/(-30)-(1)/(-60))=(-1)/(120)`
`rArrf_(4)=-120cm` (diverging)