A symmetric double convex lens of power 4D is cut in two halves by plane perpendicular to the principal axis. The power of each half is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2D
By the lens maker’s formula the power of a lens is \( P = (\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \). For the symmetric double convex lens \( R_1 = R \) and \( R_2 = -R \).
\( \displaystyle P = (\mu-1)\left(\frac{1}{R}+\frac{1}{R}\right) = \frac{2(\mu-1)}{R} = 4\,\mathrm{D} \Rightarrow \frac{\mu-1}{R} = 2\,\mathrm{D} \)
A cut by a plane perpendicular to the axis passes through the middle of the lens and leaves two plano-convex lenses, each with one curved face of radius R and one plane face (\( R_2 = \infty \)).
\( \displaystyle P' = (\mu-1)\left(\frac{1}{R}-\frac{1}{\infty}\right) = \frac{\mu-1}{R} = 2\,\mathrm{D} \)