Question

5. A monochromatic ray of light with frequency f= 6.00 x 1014 Hz is traveling in medium #1 with index of refraction ni = 1.45. It strikes the interface with medium #2 at an incident angle 0; = 15.0° with respect to the normal. The index of refraction for medium #2 is n2 = 1.30. (a) What are the speed and wavelength of the initial ray of light? (b) What is the frequency of the transmitted ray of light? (c) What are the speed and wavelength of the transmitted ray of light? (d) What is the angle of transmission, 0,?

Answer 1

According to Snellis low, ng sin Of = n, sin on where n = index of refraction for medium #1 n = index of refraction for medium #2 O, index of incident angle 0,= transmitted angle n sin o, = sin or rearranging 1. 30 sin O = De sin e Sin Or = 1.45 x sin ( 15.0°) sin O = 1.115 3 * 0.2588 sin O₂ = 0,2886 O₂ = sint (0.2886) On = 16.6545 ..Angle of transmitti transmission. @t-on: 16,6545

The speed of the initial and transmitted ray of light is, v=C = 3x108 m/s ni 1.45 Vi = 2.0689x10mts Initial speed. Vq = 3x10 m/s . 1.30 V = 2.3076x10mis transmitted speed transmitted The wavelength of the initial and ray is light is, V = fx & A- f - 6.00% LO4 H₂ 2,= vi a = 2.0689*10mis 6.00x1014 Hz x = 0.3448 x 10-14 to 2 = 0.3448x 108-14) m 2,= 0.3448x 10-6 m. 2,= 3448x 10-10 m 1,= 3448 A

V = f = 22 - a = 2.30768 108 m/s 6.00x1014 Hz (8-14) no 2= 0.3846 X108 = 0.3846x10-6 m 123846X10-10 m 2 = 3846 A (6) Answer for (6) - I wave of light of single frequency to Cor wavelength x is called monochromatic ray of light In such a case, the frequency of both incident and transmitted ray of light will remain same. . Hence, f = F2 = f = 6.00 x 1014 Hz.