A thin plano-convax lens fits exactly into a plano concave lens with their plane surface parallel to each other as shown in the figure.the radius of the curvature of the curved surface `R=30cm` The lens ar made of different material having refractive index`mu_(1)=(3)/(2)`and `mu_(2)=(5)/(4)`as shown in the figure

(i) if plane surface of hte plano -convex lens is silvered,then calculate the equivalent focal length of this system and also calculate the nature of the is equivalent mirror .
(ii) An object having transverse length `5cm`inplaced ont he axis of equivalenet mirror(in part1)`at a distance`15cm` from the equivalent mirror alone principal axis.Find teh transverse magnification prodcuied by equivalents mirror.

Answer

`+60,+4//5`

Explanation

`(1) P_(eq)=2P_(l_1)+2P_(l2)+P_(m)….(1)`
`(1)/f_(l_1)=((3)/(2)-1)((1)/(oo)-(1)/(30))`
`f_(l_1)=-60cm rArr P_(l_1)=(100)/(f_(l_1)) rArr P_(l_1)=-(5)/(3)D`
`(1)/f_(l_2)=((5)/(4)-1)((1)/(30)-(1)/(oo)) rArr (1)/(f_(l_2))=(1)/(120)`
`f_(l_2)=120cm rArr P_(l_2)=(5)/(6)D`
`P_(m)=0` since `f_(m)=oo rArr P_(eq)=2P_(l_1)+2P_(l_2)+P_(m)`
`P_(m)=(-10)/(3)+(10)/(6)+0 rArr P_(eq)=-(10)/(6)D`
`F_(eq)=60cm `
(ii)`m=(h_(2))/(h_(1)) =-(v)/(u)=(f)/(f-u) rArr m=(f)/(f-u)`
`m=(60)/(60-(-15)) rArr m=(60)/(75)`
`m=(4)/(5)`