Question

A plano-convex lens (=1.5) of aperture diameter 8 cm has a maximum thickness of 4 mm. The focal length of the lens relative to air is

Answer 1

Explanation:

See figure, here it is shown that A plano convex lens of thickness 1mm and diameter of its aperture is 4cm or 40mm.

so, AB = radius of aperture = 20mm

PC = radius of curvature = R

then, BC = (R - 1) mm

and AC = radius of curvature = R

use Pythagoras theorem,

AC² = AB² + BC²

R² = 20² + (R - 1)²

R² = 400 + R² + 1 - 2R

401 - 2R = 0

R = 200.5mm

hence,

and [ because 2nd surface is plane ]

now, use formula ,

= (1.5 - 1) [ 1/200.5 - 1/∞ ]

= 0.5/200.5

= 1/401

hence, f = 401 mm or 40.1 cm