The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

. The focal length of a lens is given by 1/f = (μ - 1) (1/R base 1 – 1/R base 2) ⇒ (μ - 1) = 1/f * 1/(1/R base 1 – 1/R base 2) = K/f ….(1) So, μ base r – 1 = K/100 …(2) Μ base y – 1 = K/98 ….(3) And μ base v – 1 = K/98 (4) So, Dispersive power = ω = μ base v - μ base r/ μ base y – 1 = (μ base v - 1) – (μ base r - 1)/( μ base y - 1) = K/96 – K/100/K/98 = 98 * 4/9600 = 0.0408

Sol. The focal length of a lens is given by 1/f = (μ - 1) (1/R base 1 – 1/R base 2) ⇒ (μ - 1) = 1/f * 1/(1/R base 1 – 1/R base 2) = K/f ….(1) So, μ base r – 1 = K/100 …(2) Μ base y – 1 = K/98 ….(3) And μ base v – 1 = K/98 (4) So, Dispersive power = ω = μ base v - μ base r/ μ base y – 1 = (μ base v - 1) – (μ base r - 1)/( μ base y - 1) = K/96 – K/100/K/98 = 98 * 4/9600 = 0.0408