Find the focal length of equivalent system shown in Figure.

Answer

`100/12 cm`

Explanation

Here radius of curvatures of different surfaces and refractive index are given, we can calculate focal lengths of lenses by using
`(1)/(f_(1))=((3)/(2)-1)((1)/(10)+(1)/(10))=(1)/(2)xx(2)/(10)=(1)/(10)`
`(1)/(f)=(mu_(1)-1) ((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_(2))=((6)/(5)-1)((_1)/(10)-(1)/(20))= (1)/(5)xx((-30)/(10xx20))= (-3)/(100)`
`(1)/(f_(3))=((8)/(5)-1)((1)/(20)+(1)/(20))=(3)/(50)`
Hence, equivalent focal length
`(1)/(f)=(1)/(f_(1)) +(1)/(f_(2))+(1)/(f_(3))=(1)/(10)+(-3)/(100)+(3)/(50)`
`rArr f=100//13 cm`