A convex lens has 12 cm focal length in air. What is its focal length in watr ? (Refractive index of air water is 1.33, refractive index for air glass =1.5)

Explanation

`""^(a)mu_(g)=1.5`
`""^(a)mu_(w)=1.33`
`f_("air")=12cm`
`f_(w)=?`
`1/(f_("air"))=(""^(a)mu_(g)-1)(1/(R_(1))-1/(R_(2)))`
`1/12=(1.5-1)(1/(R_(1))-1/(R_(2)))`
`1/12=0.5(1/(R_(1))-1/(R_(2)))`
`(1/(R_(1))-1/(R_(2)))=1/(12xx0.5)=1/6`
Now `1/(f_(w))=(""^(w)mu(g)-1)(1/(R_(1))-1/(R_(2)))`
`1/(f_(w))=((""^(a)mu_(g))/(""^(a)mu_(w))-1)(1/(R_(1))-1/(R_(2)))`
`=(1.5/1.33-1)1/6`
`1/(f_(w))=((1.5-1.33)/1.33)1/6=0.17/1.33xx1/6`
`impliesf_(w)=(1.33xx6)/0.17=46.96cm`