When the curved surface of the lens (refractive index `mu` ) is in contact with the table, the image of the bottom-most point of lens (in glass ) is formed due to refraction at plane face. The image of O appears at `I_(1)` .
Here, ` u_(1)=AO=-4cm, v_(1)=AI_(1)=3cm,`
`mu_(1)=mu`, and `mu_(2)=1`, and `R_(1)=oo`
`:. (mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R_(1))` gives `(1)/(-3)-(mu)/(-4)=(1-mu)/(oo)` (i)
When the plane surface of the lens is in contact with the table, the image of center of the plane face if formed due to refraction curved surface. The image of O is formed aaaaaaaat `I_(2)`.
Here, `u=AO=-4cm, upsilon=AI_(2)=-25//8cm`
`mu_(1)=mu, mu_(2)=1`, and `R_(2)=-R`
`:. mu_(2)/v_(2)-mu_(1)/mu_(2)=(mu_(2)-mu_(1))/R_(2)`
Gives `(1)/((-(25)/(8)))-(mu)/(-4)=(1-mu)/(-R)`
From Equ. (i), `mu=4//3`, therefore this equation gives
`-(8)/(25)+(4//3)/(4)=-((1-(4)/(3)))/ (R)-(8)/(25)+(1)/(3)=(1)/(3R)` or `(1)/(75) =(1)/(3R)`
This gives `R=25 cm`.
The focal length (f) of plano-convex lens `(R_(1) =R " and " R_(2)=oo)`
is `(1)/(f) =(mu-1)((1)/(R)-(1)/(oo))=(mu-1)/(R)=((4)/(3)-1)/(25)=(1)/(75)rArr f=75cm`