Question

Figure shows a transparent hemisphere of radius $3.0\text{cm}$ made of a material of refractive index $2.0$. A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Find the location of the image formed after the refraction at the first surface among the points given in the options.

• A. $B$
• B. $B^{{}^{\prime }}$
• C. $A$
• D. $C$

Answer 1

The correct option is B $B^{{}^{\prime }}$


Here, $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\Rightarrow \frac{2}{v}-\frac{1}{-\infty }=\frac{2-1}{3}$
[For parallel rays, $u=-\infty$]
$\Rightarrow \frac{2}{v}=\frac{1}{3}\Rightarrow v=6\text{cm}$
Hence, if the sphere is completed, image is formed diametrically opposite of $A$ (at $B^{\prime }$).

Why the question? Caution: Remember that +ve distance is taken along the direction of light ray.