Question

A double concave lens has to be made from crown glass. How much should the radii of surfaces of lens be kept to make the power of lens -2.5 D? Refractive index of crown glass is 1.65. 
 

Hint:

For a concave lens, both radii of curvature are negative, and the formula for the focal length is derived using the refractive index and surface curvatures.

Answer 1

The power of a lens is given by the lens formula: \[ P = \frac{1}{f}, \] where \( f \) is the focal length of the lens. The focal length for a lens with radii of curvature \( R_1 \) and \( R_2 \) is given by the lensmaker's formula: \[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right), \] where \( \mu \) is the refractive index of the material of the lens. Since it is a double concave lens, \( R_1 \) is negative and \( R_2 \) is also negative. Given the power \( P = -2.5 \, \text{D} \), the focal length is: \[ f = \frac{1}{P} = -0.4 \, \text{m}. \] Substituting the known values, we can find the radii of the surfaces using the lensmaker's formula.