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 (in m) 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`