Two thin similar watch glass pieces are joimed together,front to front ,woth near convex portion silvered and the combination of glass pieces is placed at a distanc e`a=60cm` from a screen.A small object is placed normal to the optical axis of the combination such that its two water`mu=4//3`,calcuated the distance through,which the object must eb displayed so that a sharp image is again formed on the screen.

Answer

`15cm`towards the combination

Explanation

First It is concave mirror
`m=(h_(2))/(h_(1))=-(v)/(u) implies -2=-(v)/(u)`
`v=2u rArr -60=2u rArr u=-30`
Applying mirror formula
`(1)/(v)+(1)/(u)=(1)/(f) rArr (1)/(-60)+(1)/(-30) =(1)/(f)`
`(1)/(f)=(-1-2)/(60) rArr f=-20cm rArr R=-40cm`
` P_(m)=-(100)/(f) rArr P_(m) =5D`
When the liquid in filled it will become a combination of convex lens and concave mirror `P_(eq)=2P_(l)+P_(m)`
` (1)/(f_(l))=(._(a)mu_(l)-1)((1)/(R_(1))-(1)/(R_(2))) rArr (1)/(f_(l))=(2(._(a)"mu_(l)-1))/(R )`
`(1)/(f_(l))=(2(4//3-1))/(40) rArr (1)/(f_(l))=(1)/(60) rArr f_(l)=60cm rArr P_(l)=(5)/(3) D" " P_(eq)=2P_(l)+P_(m) rArr P_(eq)=2xx(5)/(3)+5 rArr P_(eq)=(25)/(3)D`
`f_(eq)=(100)/(-P_(eq)) rArr f_(eq)=(1000)/(-25//3)rArr f_(eq)=-12 cm`
to form image again on screen
`(1)/(-60)+(1)/(u_(2))=(1)/(-12) rArr (1)/(u_(2))=(1)/(60)-(1)/(12) rArr (1)/(u_(2))=(+1-5)/(60)`
`u_(2)=-15cm`
Shift=`(30-15)`
Shift =`15`towards the combination.