Question

An extended object of size $2\text{cm}$ is placed at a distance of $10\text{cm}$ in air $(n=1)$ from the pole on the principal axis of a spherical curved surface. The medium on the other side of the refracting surface has refractive index $n=2$. Find the position, nature and size of the image formed after single refraction through the curved surface.

• A. $30\text{cm}$ from pole in the medium having refractive index $1$, virtual, erect and $4\text{cm}$ in size.
• B. $40\text{cm}$ from pole in the medium having refractive index $1$, virtual, erect and $4\text{cm}$ in size.
• C. $40\text{cm}$ from pole in the medium having refractive index $1$, real, inverted and $4\text{cm}$ in size.
• D. $30\text{cm}$ from pole in the medium having refractive index $1$, real, inverted and $4\text{cm}$ in size.

Answer 1

The correct option is B $40\text{cm}$ from pole in the medium having refractive index $1$, virtual, erect and $4\text{cm}$ in size.


We know,
$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$
$\Rightarrow \frac{2}{v}-\frac{1}{(-10)}=\frac{2-1}{20}$
$\Rightarrow v=-40\text{cm}$

Magnification, $m=\frac{h_i}{h_o}=\frac{n_{1}v}{n_{2}u}=\frac{1\times -40}{2\times -10}=+2$
$\Rightarrow$Magnified, virtual and erect.

Also, $h_i=m\times h_o=(+2)\times (+2)=+4\text{cm}$

Therefore, image is formed at $40\text{cm}$ from pole in the medium having refractive index $1$, virtual, erect and $4\text{cm}$ in size.