Question

Position of the final image of an object $\text{O}$ (as shown in the figure) with respect to the plane surface will be

• A. $14\text{cm}$ below
• B. $14\text{cm}$ above
• C. $21\text{cm}$ below
• D. $21\text{cm}$ above

Answer 1

The correct option is A $14\text{cm}$ below

GIVEN:
perpendicular distance from plane surface $h=10\text{cm}$
thickness of glass slab $t=3\text{cm}$
refractive index of material $\mu =3/2$

For refraction through glass slab,

$h_{app}=\mu h_{real}$

$\Rightarrow h_{app}=\frac{3}{2}\times 10=15\text{cm}$

Other end of the glass slab is made reflecting (plane mirror).

So, apparent distance of the object from the mirror $=15\text{cm}+3\text{cm}=18\text{cm}$.

Thus, mirror will from image at $18\text{cm}$ below it or $21\text{cm}$ below the plane surface.

Now again for image, when viewed from object side,
$d_{app}=\frac{d_{real}}{\mu }$

$\Rightarrow d_{app}=\frac{21}{3/2}=14\text{cm}$.
i.e Image will appear $14\text{cm}$ below plane surface.

Hence, $\left(a\right)$ is the correct option.