The radii of curvature of the faces of a double convex lens of focal length 12 cm made up of glass (\( \mu = 1.5 \)) are 10 cm and ‘p’ cm respectively. The value of p is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 cm
Use the lens maker’s formula with the sign convention that distances are positive along the direction of the incident light. For a double convex lens the first surface has \( R_1 = +10\,\mathrm{cm} \) and the second has \( R_2 = -p \).
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( \displaystyle \frac{1}{12} = (1.5 - 1)\left(\frac{1}{10} + \frac{1}{p}\right) \)
\( \displaystyle \frac{1}{10} + \frac{1}{p} = \frac{1}{6} \Rightarrow \frac{1}{p} = \frac{1}{6} - \frac{1}{10} = \frac{1}{15} \)
\( p = 15\,\mathrm{cm} \)