Question

Refractive index of the medium on the left and right side of the spherical surface are $1$ and $1.5$ respectively. For the arrangement of object and spherical refracting surface as shown in figure, the position of image will be

• A. $+20\text{cm}$
• B. $+45\text{cm}$
• C. $-45\text{cm}$
• D. $+30\text{cm}$

Answer 1

The correct option is B $+45\text{cm}$

Suppose the image of the object $O$ forms at $I$. The ray diagram can be drawn as:


Given,
${\mu }_1=1$
${\mu }_2=1.5$
The direction of incident ray is taken positive as per sign convention.

For refraction at the spherical surface we can use,
$R=+6\text{cm}$
$u=-20\text{cm}$

Let the image distance be $v$

Using relation between object and image distance for refraction at curved surfaces:

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{1.5}{v}-\frac{1}{(-20)}=\frac{1.5-1}{+6}$

$\text{Or,}\frac{1.5}{v}=\frac{1}{12}-\frac{1}{20}$

$\Rightarrow$ $v=\left(\frac{12\times 20}{20-12}\right)\times 1.5$

$\therefore v=\frac{240}{8}\times 1.5=45\text{cm}$

The $+ve$ sign of image distance represents that image is formed in the direction of incident light.

Why this question ? It intends to test your understanding of application of sign convention.