Question

A plano-convex lens of focal length $16 \, \text{cm$ is made of a material of refractive index $1.4$. Calculate the radius of the curved surface of the lens.}

Hint:

For plano-convex lenses, use the lens maker's formula and remember that one radius of curvature is $\infty$ for the plane surface.

Answer 1

The lens formula is stated as: \[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Given a lens with a refractive index of \(\mu = 1.4\), the formula simplifies to: \[ \frac{1}{16} = (1.4 - 1) \left( \frac{1}{R} - \frac{1}{\infty} \right) \] As \(\frac{1}{\infty} = 0\), the equation reduces to: \[ \frac{1}{16} = 0.4 \times \frac{1}{R} \] Solving for \(R\): \[ R = 16 \times 0.4 = 6.4 \, \text{cm} \] Therefore, the radius of the curved surface is \(6.4 \, \text{cm}\).