Question

1. The diagram at right illustrates the refraction of a wave as it propagates from a medium of larger wave speed into a medium of slower wave speed. Larger wave speed Incident wavefronts theta_i ?_i Smaller wave speed ?_r Refracted wavefronts theta_r a. Use trigonometry to determine the mathematical relationship between the angle of incidence (?_i), the angle of refraction (?_r), the wavelength of the incident wave (?_i), and the wavelength of the refracted wave (?_r). Show your work. b. Starting from the equation that you wrote above, derive a mathematical formula relating ?_i, ?_r, v_i, and v_r, where v_i and v_r are the propagation speeds of the incident and refracted wave, respectively. Show your work.

          1. The diagram at right illustrates the refraction of a wave as it propagates from a medium of larger wave speed into a medium of slower wave speed.

Larger wave speed
Incident wavefronts
theta_i
?_i
Smaller wave speed
?_r
Refracted wavefronts
theta_r

a. Use trigonometry to determine the mathematical relationship between the angle of incidence (?_i), the angle of refraction (?_r), the wavelength of the incident wave (?_i), and the wavelength of the refracted wave (?_r). Show your work.

b. Starting from the equation that you wrote above, derive a mathematical formula relating ?_i, ?_r, v_i, and v_r, where v_i and v_r are the propagation speeds of the incident and refracted wave, respectively. Show your work.

$1. The diagram at right illustrates the refraction of a wave as it propagates from a medium of larger wave speed into a medium of slower wave speed. Larger wave speed Incident wavefronts thetai ?i Smaller wave speed ?r Refracted wavefronts thetar a. Use trigonometry to determine the mathematical relationship between the angle of incidence (?i), the angle of refraction (?r), the wavelength of the incident wave (?i), and the wavelength of the refracted wave (?r). Show your work. b. Starting from the equation that you wrote above, derive a mathematical formula relating ?i, ?r, vi, and vr, where vi and vr are the propagation speeds of the incident and refracted wave, respectively. Show your work.$

Added by Nicholas B.

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