The bottom of glass beaker is made of a thin equiconvex lens having bottom side silver polished as shown in figure,. Now the water is filled in the baker upto a height of `h=4m.` The image of point object floating at middle point of beaker at the surface of water coincides with it. Find out the value of radius of curvature of lens. `(._amu_(g)=3//2, ._amu_(w)=4//3)`

Answer

5m

Explanation

Power of equivalent mirror,`P_(M)^(')=2P_(2)+P_(M)`
`(1)/(f_(2))=((3//2)/(4//2)-1)((1)/(R)+(1)/(R))=(1)/(8)xx(2)/(R)=(1)/(4R)`
`f_(2)=4R` and `P_(2)=(1)/(4R)`
`-(1)/(f_(m)^('))=2xx(1)/(4R)+(2)/(R)=(5)/(2R)`
`f_(m)^(')=-(2)/(5)R`
`|h|=2|f_(m)^(')|`
`h=2xx(2)/(5)R=4m`
`R=5m`