The focal length of a convex lens of glass `(mu = 1.5)` in air is 30 cm. Find its focal length when the lens is placed in water `(mu = 4//3)`.

Options

A. `20` cm
B. `30` cm
C. `40` cm
D. `25` cm

Answer

C

Explanation

According to lens maker.s formula,
The focal length of the lens in air is
`(1)/(f_("air"))=((mu_(l))/(mu_(a))-1)((1)/(R_(1))-(1)/(R_(2)))=((3//2)/(1)-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_("air"))=(1)/(2)((1)/(R_(1))-(1)/(R_(2)))` …(i)
The focal length of the lens in water is
`(1)/(f_("water"))=((mu_(l))/(mu_(w))-1)((1)/(R_(1))-(1)/(R_(2)))=((3//2)/(4//3)-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_("water"))=(1)/(8)((1)/(R_(1))-(1)/(R_(2)))` ...(ii)
Dividing (i) by (ii), we get `(f_("water"))/(f_("air"))=4`
`f_("water")=4xxf_("air")=4xx10` cm= `40` cm