Question

A parallel beam of light falls successively on a thin convex lens of focal length $40cm$ and then on a thin convex lens of focal length $10cm$ as shown in Fig. (a)
In figure (b) the second lens is an equiconcave lens of focal length $10cm$ and made of a material of refractive index $1.5$. In both cases, the second lens has an aperture equal to $1cm$.
Now, a liquid of refractive index $\mu$ is filled to the right of the second lens in case $B$ such that the area illuminated in both the cases is the same. Determine the refractive index of liquid.

• A. $1$
• B. $2.5$
• C. $3$
• D. $1.5$

Answer 1

The correct option is C $3$

Given: A parallel beam of light falls successively on a thin convex lens of focal length 40 cm and then on a thin convex lens of focal length 10 cm. The second lens is an equiconcave lens of focal length 10 cm and made of material of refractive index 1.5. In both the cases, the second lens has an aperture equal to 1 cm. Now, a liquid of refractive index $\mu$ is filled to the right of the second lens in case B such that the area illuminated in both the cases is the same.

To find the refractive index of the liquid.

Solution:

When liquid of refractive index $\mu$ is filled to the right of this lens, the first surface of the lens (radius of curvature = 10cm) forms the image at the object only. Considering the refraction at the second surface

$\frac{\mu }{\infty }-\frac{1.5}{-10}=\frac{\mu -1.5}{10}$ (therefore, same area $⟹v\to \infty$)

$⟹\mu -1.5=1.5⟹\mu =3$

is the required refractive index of the liquid.