Question

A double-convex lens, with each face having the same radius of curvature \( R \), is made of glass of refractive index \( n \). Its power is:

Hint:

For a double-convex lens, use the lens maker's formula with the radii of curvature appropriately signed. The total power is proportional to the refractive index and inversely proportional to the radius.

Answer 1

The lens maker’s formula is expressed as: \[ \frac{1}{f} = (n-1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right) \] For a double-convex lens with identical radii of curvature \( R \) for both surfaces, the formula simplifies to: \[ \frac{1}{f} = (n-1) \left(\frac{1}{R} - \frac{-1}{R}\right) \] This further reduces to: \[ \frac{1}{f} = (n-1) \cdot \frac{2}{R} \] The power \( P \) of the lens is defined as: \[ P = \frac{1}{f} = \frac{2(n-1)}{R} \]