JEE Main 2025 Apr 2 Shift 1, Physics Q17: Refraction at Plane and Spherical surfaces

Apply the refraction formula at a single spherical surface using the standard sign convention (distances measured from the pole, positive to the right):

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

Here ${\mu }_1=1$, ${\mu }_2=1.5$, $u=-0.2\text{m}$ (object on the left), $R=+0.4\text{m}$ (C on the right of the pole).

$$\frac{1.5}{v}-\frac{1}{-0.2}=\frac{0.5}{0.4}$$

$$\frac{1.5}{v}+5=1.25$$

$$\frac{1.5}{v}=-3.75\Rightarrow v=-0.4\text{m}$$

The negative sign means the image lies on the same side as the object, i.e. 0.4 m to the left of the spherical surface (virtual image).

$\therefore$ Option (2) is correct.