A thin film that is \(175 \mathrm{~nm}\) thick and has an index of refraction smaller than 1.56 covers the front surface of a vertical sheet of glass that has an index of refraction of 1. 56. The back surface of the glass interfaces with air, as does the front surface of the film. When a beam of light of variable wavelength is normally incident on the front surface of the film, we observe that, as the wavelength of the light is varied, \(473-\mathrm{nm}\) light reflects strongly from the front film surface. We also determine that if the film is any thinner than \(175 \mathrm{~nm}\), no constructive interference occurs. When the beam direction is changed so that the angle of incidence at which the light strikes the air-film interface is \(51.0^{\circ}\), what is the angle of refraction for the beam in the film?