When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is 45 cm from the lens is formed 36 cm above the lens. When a liquid is poured in the tank to a depth of 40 cm, the distance of the image of the mark above the lens is 48 cm. The refractive index of the liquid is

• A

  1.358
• B

  1.544
• C

  1.472
• Correct answer
  D

  1.366

Solution

Initially without water, $\frac{1}{36}-\frac{1}{-45}=\frac{1}{f} \Rightarrow f=20$ then, after pouring water upto 40 cm
apparent object distance $=\frac{40}{\mu}+5, \frac{1}{48}+\frac{1}{\frac{40}{\mu}+5}=\frac{1}{20} \Rightarrow \mu=1.366$

Hence, the correct answer is option: 'D'.