This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and interpret the angle of incidence. The glancing angle is 60^. The angle of incidence i is measured from the normal, so: i = 90^ - 60^ = 30^ Given frequency of light in air, f_air = 5.0 × 10^14 Hz. Given speed of light in air, c = 3.0 × 10^8 m/s. Given refractive index of glass, n_g = 1.6. The refractive index of air, n_air = 1. a) Frequency of the light in the prism The frequency of light remains constant when it passes from one medium to another. f_prism = f_air f_prism = 5.0 × 10^14 Hz The frequency of the light in the prism is 5.0 × 10^14 Hz. b) Wavelength of the light in air The relationship between speed, frequency, and wavelength is c = f . _air = (c)/(f_air) Substitute the values: _air = 3.0 × 10^8 m/s5.0 × 10^14 Hz _air = 0.6 × 10^-6 m _air = 6.0 × 10^-7 m The wavelength of the light in air is 6.0 × 10^-7 m. c) Wavelength of the light in the prism The refractive index is also given by the ratio of wavelengths: n_g = _air_prism. _prism = _airn_g Substitute the values: _prism = 6.0 × 10^-7 m1.6 _prism = 3.75 × 10^-7 m The wavelength of the light in the prism is 3.75 × 10^-7 m. d) Angle of refraction Use Snell's Law: n_air i = n_g r. 1 · (30^) = 1.6 · r r = ((30^))/(1.6) r = (0.5)/(1.6) r = 0.3125 r = (0.3125) r ≈ 18.21^ The angle of refraction is 18.21^. e) Speed of the light in the block The refractive index is defined as n_g = (c)/(v_prism), where v_prism is the speed of light in the prism. v_prism = (c)/(n_g) Substitute the values: v_prism = 3.0 × 10^8 m/s1.6 v_prism = 1.875 × 10^8 m/s The speed of the light in the block is 1.875 × 10^8 m/s. Send me the next one 📸