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  4. A point object is placed at a distance of 62 cm from a concave mirror of focal length 20 cm. A slab of the thickness 6 cm and refractive index μ=3 / 2 is placed in between the object and the mirror at a distance 1.5 cm from the mirror. The distance (in cm ) of the final image from the mirror is

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Q. A point object is placed at a distance of $62 \,cm$ from a concave mirror of focal length $20\, cm$. A slab of the thickness $6 \,cm$ and refractive index $\mu=3 / 2$ is placed in between the object and the mirror at a distance $1.5\,cm$ from the mirror. The distance (in $cm$ ) of the final image from the mirror is

Ray Optics and Optical Instruments

Solution:

Shift, $x=t\left(1-\frac{1}{\mu}\right)=6\left(1-\frac{1}{\frac{3}{2}}\right)=2 \,cm$
$\Rightarrow u$ for mirror $=62-2=60\, cm$
Now,
$\frac{1}{v}-\frac{1}{60}=-\frac{1}{20} $
$v=-30 \,cm$
The final image will be formed at $32 \,cm (30+2)$.