A thin lens made of glass of refractive index `mu = 1.5` has a focal length equal to 12 cm in air. It is now immersed in water (`mu=4/3`). Its new focal length is

Explanation

`(f_(a))^(-1)=(""^(a)mu_(g)-1)(1/R_(1)-1/R_(2))`
`(f_(w))^(-1)=(""^(w)mu_(g)-1)(1/R_(1)-1/R_(2))`
`therefore(f_(w))/(f_(a))=(""^(a)mu_(g)-1)/(""^(w)mu_(g)-1)=(""^(a)mu_(g)-1)/((""^(a)mu_(g))/(""^(a)mu_(w))-1)=(3/2-1)/((3/2)/(4/3)-1)=(1/2)/(9/8-1)=(1/2)/(1/8)=1/2xx8/1=4`
`thereforef_(w)=4f_(a)=4f`