A lens with a focal length of `f=30 cm` produces on a screen a sharp image of an object that is at a distance of `a=40 cm` from the lens. A plane parallel plate with thickness of `d=9 cm` is placed between the lens and the object perpendicular to the optical axis of the lens. Through what distance should the screen be shifted for the image of the object to remain distinct? The refractive index of the glass of the plate is `mu=1.8.`

Answer

A, C

Explanation

Using lens formula, `1/v-1/u=1/f`
`1/(v_1)-1/(-40)=1/30`
`:. v_1=120 cm`
Shift due to the slab,
`Deltax=(1-1/mu)d=(1-1/1.8)9=4 cm`
`:. u'=-(40-Deltax)`
`=-36 cm`
`:. 1/(v_2)-1/(-36)=1/30`
`:. v_2=180 cm`
Therefore, we will have to shift the screen a
distance`x=v_2-v_1=60 cm` away from lens.