Refractive index of glass slab shown in figure is `1.5.` Focal length of mirror is `20cm`. Find
(a) total number of reflections before final image is formed.
(b) reduced steps.
(c) value of x, so that final image coincides with the object.

Answer

B, C, D

Explanation

(a) There are total four refraction and one reflection.
(b) Reduced steps are three, first slab , then mirror and then again slab.
(c) Shift due to the slab,
` s=\(1-(1)/(mu))t=(1-(2)/(3))(9)=3`cm
Actual distance from mirror to object is `(19+x)`cm Slab will reduce this distance by 3cm.
So, apparent distance will be `(16+x)cm`
Now, if `16+x=R=2f=40`cm or `x=24`cm
then ray of light will fall normal to the cancave mirror. It will retrace its path and final image will coincide with the object
`x=24`cm