The radius of curvature of each surface of a double convex lens is 15 cm and the refractive index of the medium of the lens is 1.5. What is the focal length of the lens ?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15 cm
Use the lens maker’s formula. For a double convex lens the first surface faces the incoming light with its centre of curvature on the far side, so \( R_1 = +15\,\mathrm{cm} \) and \( R_2 = -15\,\mathrm{cm} \).
\( \displaystyle \frac{1}{f} = (\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \)
\( \displaystyle \frac{1}{f} = (1.5-1)\left(\frac{1}{15}+\frac{1}{15}\right) = 0.5\times\frac{2}{15} = \frac{1}{15}\,\mathrm{cm^{-1}} \)
\( f = 15\,\mathrm{cm} \)