Question

A point object is placed $33$ cm from a convex mirror of curvature radius $=40$ cm. A glass plate of thickness $6$ cm and index $2.0$ is placed between the object and mirror, close to the mirror. The distance of final image from the object is

• A. $90cm$
• B. $35cm$
• C. $36cm$
• D. $45cm$
• E. None of these

Answer 1

The correct option is D $45cm$

object distance from lens is 33 cm , but due to thin slab a deviation is occurred due to which the object is shifted toward the lens by a distance t/mu (t is the thickness of slab and mu is refractive index of slab)

shift = $\frac{6}{2}$ = 3 cm

new distance of object is 33-3 = 30 cm

$u=-30cm$ and $f=20cm$ and $v=?$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{30}=\frac{1}{20}$

$\frac{1}{v}=\frac{1}{30}+\frac{1}{20}$

$\frac{1}{v}=\frac{5}{60}$

$v=12cm$.(virtual image)

distance between object and image is $33+12=45cm$