Question

A slab of glass of thickness $5cm$ and refractive index $1.5$ is held a few centimeter in front of a concave mirror of radius of curvature $40cm$. The faces of the slab being perpendicular to the principal axis of the mirror. How far (in $cm$) from the mirror must a small object be placed if its image coincides with the object? [consider all events].

Answer 1

Answer: 41.67

Object shift due to slab
$=5\left(1-\frac{2}{3}\right)=\frac{5}{3}=1.67cm$
Now, so as the image of object coincides with it, the object must be placed of distance $40cm$ from pole (if slab was absent), but as slab shifts the object apparently by $1.67cm$ towards the mirror. So the object must be placed at distance $41.67cm$ from the mirror.