Question

A glass slab has a length of $6cm$ and refractive index $\mathrm{1.5.}$ One of the outer surfaces of the slab is silvered and object is placed at a distance of $10cm$ from the other end. The image formed in the mirror will be at a distance of _____ from the object.

• A. $20cm$
• B. $32cm$
• C. $28cm$
• D. $38cm$

Answer 1

The correct option is A $20cm$

Thickness of plate $\left(t\right)=6$

Distance of object $\left(\mu \right)=10$

Distance of image $\left(x\right)=?$

$x+\mu =v+t-x$

$2x=\left(v+t+\mu \right)$

$x=\frac{\left(v+t+\mu \right)}{2}$

$\text{Refractive index}=\frac{\text{Real depth}}{\text{app}\text{.depth}}=\frac{t}{x}$

$1.5\left(v+\mu +t\right)=2t$

$v+\mu +t=\frac{2}{1.5}=8$

$v=7-\left(u+t\right)$

$v=7-10-6=9$

Image $=-\left(9+6\right)-4$

$=\left(-20\right)$