A point object O is placed in front of a concave mirror of focal length 10cm. A glass slab of refractive index `mu=3//2` and thickness 6cm is inserted between the object and mirror.

Q. Find the position and nature of the final image when the distance x shown in figure, is 5cm.

Options

A. 11cm, virtual
B. 17cm, real
C. 14cm, real
D. 20cm, virtual

Answer

b.

Explanation

The normal shift produced by a gless slab is,
`Deltax=(1-(1)/(mu))t=(1-(2)/(3))(6)=2cm`
i.e., for the mirror, the object is placed at a distanced `(32-Deltax)=30cm` from it.
Applying mirror formula,
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/(30)=-(1)/(10)`
or, `v=-15cm`
a. when `x=5cm:` The light falls on the slab on its return journey as shown. But the slab will again shift it by a distance
`Deltax=2cm` . Hence the final real image is formed at a distance `(15+2)=17cm` from the mirror.

b. When `x=20cm:` This time also the final image is at a distance of 17cm from the mirror but it is virtual as shown.
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