A point object is placed on principal axis of a concave mirror of radius of curvature `20 cm` at a distance `31 cm` from poll of the mirror. `A` glass slab of thikness `3 cm` and refractive index `1.5` is placed between object and mirror as shown in the figure. Find the distance (in `cm`) of final image formed by the system from the mirror.

Answer

16

Explanation

Apprent shift in position of the object due to refraction through the slab `=d(1-(1)/(mu_(rel)))`
`=3(1-(1)/(3/2))=1 cm ` towards the mirror,
Now, for reflection from the mirror,
`u=-30 cm f=-(R)/(2)=-10 cm`
`therefore` `(1)/(v)=(1)/(f)-(1)/(u)` gives `(1)/(v)=-(1)/(10)-(1)/((-30))` `therefore v=-15 cm`
Thus is formed `15 cm` , right of the mirror but because of second refraction through the slab the image is shifted `1 cm` away from the mirror. Hence final image is formed at a distance `16 cm` away from mirror.