Explain

An object is placed 21cm in front of concave mirror of radius of curvature 10 cm. A glass slab of thickness 3 cm and RI 1.5 is then placed close to the mirror in the space between the object and mirror. Find the position of final image formed.

the position of the object as well as the image will change due to presence of the glass slab as it causes refraction of the light rays. 

Now, the shift in the position of the image will be shown sing the following image

The image is positioned at O but due to the refraction from glass slab it will be shifted to O' as seem by the mirror. So, the new image distance will be

u = O'P = OP - OO'

now OO' = t.(1 - 1/u)

here t = 3cm  and u = 1.5

so,

OO' = 3.[1 - (1/1.5)]

or

OO' = 1 cm

so, the image distance will be

u = 21cm - 1cm = 20 cm