A convex lens of refractive index 1.5 has a focal length of 18 cm in air. Calculate the change in its focal length when it is immersed in water of refractive index `(4)/(3)`.

Explanation

`mu_(1)=1.5`
`f_(1)=18cm`
`(1)/(f_(1))=(mu_(1)-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(18)=(1.5-1)((1)/(R_(1))-(1)/(R_(2)))" ….(i)"`
When lens is immersed in water.
`mu_(2)=(4)/(3)`
`therefore" "(1)/(f_(2))=((mu_(1))/(mu_(2))-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_(2))=((15xx3)/(10xx4)-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_(2))=((1)/(8))((1)/(R_(1))-(1)/(R_(2)))" ...(ii)"`
`(f_(2))/(18)=0.5xx8`
`f_(2)=0.5xx8xx18`
`=72cm`
Change in focal lenght `=f_(2)-f_(1)`
`=72-18`
`=54cm`