Question

1. A light beam with frequency 560 THz in air strikes a sheet of glass (n 1.8) at an angle of 50° from the surface of the glass. The glass has thickness 4 cm. What is the wavelength of the light in air and in the glass? What angle does the light beam refract upon entering and exiting the glass? How long does it take the light beam to travel through the glass?

Answer 1

Wave length (lambda), frequency (gamma) and speed (v) of a wave are related as: lambda = u/gamma In air, velocity of light is c u = c = 3 times 10^8 m/s lambda_air = 3 times 10^8 m/s/gamma gamma = 560 TH_z = 560 times 10^12 HZ lambda_air = 3 times 10^8 m/s/560 times 10^12 Hz = 5 . 357 times 10^-7 m lambda_air = 535 . 7 nm In glass of retractive index, the velocity of light is u = c/n lambda_glass = c/n/gamma = c/n gamma using c = 3 times 10^8 m/s, n = 1 . 8, gamma = 560 times 10^12 HZ lambda_glass = 2 . 976 times 10^-7 m lambda_glass = 297 . 6 nm \r\n using shells law n_air sin I, = n_galls sin r, Rightarrow sin r_1 = n_air/n_glass sin i_1 Rightarrow r_1 = sin^-1 (n_air/n_glass sin i_1) using n_air almostequalto 1, n_glass = 1 . 8, i_1 = 50 degree we get r_1 = 25 . 2 degree