Lensmakers Formula



  1. A converging meniscus lens has surfaces whose radii of curvature are 20 cm and 30 cm. The lens is made from crown glass whose index of refraction is 1.5. Find its focal length.

    2. 1/f = (n-1)(1/R1 + 1/R2)

    1/f = (1.5 - 1)(1/20 - 1/30)

    1/f = 0.5 x (1/60) = 1/120

    f = 120 cm


  2. The index of refraction of crown glass is 1.523 for blue light and 1.517 for red light. How far apart are the focal points for blue and red light of a plano-convex lens of crown glass whose radius of curvature is 200 mm ?

    3. 1/f = (n-1)(1/R1 + 1/R2)

    1/fblue = (1.523 - 1)(1/200) = 0.523/200

    fblue = 200/0.523 = 382.4 mm

    1/fred = (1.517 - 1)(1/200) = 0.517/200

    fred = 200/0.517 = 386.8 mm

    fred - fblue = 386.8 - 382.4 = 4.4 mm


  3. Both surfaces of a double-concave lens whose focal length is -18 cm have radii of 20 cm. Find the index of refraction of the glass.

    4. 1/f = (n-1)(1/R1 + 1/R2)

    R1 = R2 = R = -20 cm

    n = 1 + R/2f = 1 + (-20)/(-18 x 2)

    n = 1.555


  4. A plano-concave lens of focal length 90 mm is to be ground from quartz of index of refraction 1.55. Find the required radius of curvature.

    5. 1/f = (n-1)(1/R1 + 1/R2)

    1/R1 = 0

    R2 =(n-1)f = (1.55-1) x (-90) = -49.5 mm