What is the refractive index of a material of prism if the frequency of light wave in it is 3 10¹⁴ ~Hz . The wavelength of light in the material of prism is 8000 Å .

Step-by-step solution

The speed of light in a medium is given by the product of its frequency and wavelength. Let v be the speed of light in the material, f be the frequency, and be the wavelength. v = f Given f = 3 10¹⁴ Hz and = 8000 Å = 8000 10⁻¹⁰ m = 8 10⁻⁷ m . v = (3 10¹⁴) (8 10⁻⁷) = 24 10⁷ m/s = 2.4 10⁸ m/s . The refractive index n is defined as the ratio of the speed of light in vacuum c to the speed of light in the medium v . Taking c = 3 10⁸ m/s : n = c v = 3 10⁸ 2.4 10⁸ = 3 2.4 = 30 24 = 5 4 = 1.25 . Answer: 1.25