A point object $\mathrm{O}$ is placed on the principal axis of a convex lens of focal length $f=20 \mathrm{cm}$ at a distance of $40 \mathrm{cm}$ to the left of it. The diameter of the lens is $10 \mathrm{cm}$. An eye is placed $60 \mathrm{cm}$ to the right of the lens and a distance $h$ below the principal axis. The maximum value of $h$ to see the image is. (assume paraxial approximation to be valid here)

• A

  0
• Correct answer
  B

  $2.5 \mathrm{cm}$
• C

  $5 \mathrm{cm}$
• D

  $10 \mathrm{cm}$

Solution

$\frac{1}{\text{v}}=\frac{1}{f}+\frac{1}{\text{u}}$

  $=\frac{1}{20}-\frac{1}{40}=\frac{1}{40}$

 v = 40 cm



To locate field of view ray passing through upper end should be used. At location of eye, its height should not be below 20 tan $\theta$ from axis to see the image i.e., $20\left(\frac{5}{40}\right)=\text{2.5}cm$

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