A plane concave lens of glass \( (\mu = 1.5) \) has a radius of curvature of its curved face 50 cm. The power of the lens is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -1.0 D
The power of a lens is the reciprocal of its focal length in metres, and the focal length follows from the lens maker's formula. For a plano-concave lens the plane face has \( R = \infty \); with light incident on the curved face, that face is concave towards the light, so \( R_{1} = -50\,\mathrm{cm} \) (Cartesian sign convention).
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_{1}} - \frac{1}{R_{2}}\right) = (1.5 - 1)\left(\frac{1}{-0.5\,\mathrm{m}} - \frac{1}{\infty}\right) \)
\( \displaystyle \frac{1}{f} = 0.5 \times (-2\,\mathrm{m^{-1}}) = -1\,\mathrm{m^{-1}} \)
\( \displaystyle P = \frac{1}{f} = -1.0\,\mathrm{D} \)
The negative sign shows that the lens is diverging, as every concave lens is.