Question

A linear object AB is at a distance of 36 cm from an equi convex lens of focal length 30 cm. In front of lens there is a plane mirror which is inclined at an angle ${45}^{\circ }$ with the principal axis of the lens at a distance l = 1 m from the mirror as shown in figure. A container with water layer d = 20 cm is placed as shown in the figure. Then choose the CORRECT statement(s). Take the refractive index of water as $\frac{4}{3}$

• A. After reflection from the mirror the image of AB will be parallel to principal axis of the lens.
• B. After reflection from the mirror the image of AB will be perpendicular to principal axis of the lens.
• C. The value of H for which the sharp image of AB can be obtained at the bottom of the container is 80 cm
• D. The value of H for which the sharp image of AB can be obtained at the bottom of the container is 85 cm.

Answer 1

Answer: (A), (D)

The correct options are
A After reflection from the mirror the image of AB will be parallel to principal axis of the lens.
D

The value of H for which the sharp image of AB can be obtained at the bottom of the container is 85 cm.

For lens,
$\frac{1}{v}-\frac{1}{(-36)}=\frac{1}{30}$

For mirror

For refraction from liquid

$\frac{1}{y}=\frac{\frac{4}{3}}{20}\Rightarrow y=15cm$
Also, 80 - y + 20 = H $\Rightarrow$ H = 85 cm