A laser beam with vacuum wavelength 20 = 632.8 nm is incident at an angle of 30.0° from the vertical (in air) into a solution of corn syrup. If the beam is refracted to 19.24° from the vertical, find the following quantities: (Sketch the question; include a normal line.) a) Index of refraction of the solution b) Frequency of light in the solution c) Speed of light in the solution d) Wavelength of light in the solution

(a) 1.517

(b) 4.74 x 10^14 Hz

(c) 1.98 x 10^8 m/s

(d) 417.14 nm

Explanation:

wavelength in air, λa = 632.8 nm

Angle of incidence, i = 30 degree

angle of refraction, r = 19.24 degree

(a) According to the Snell's law

refractive index, μ = Sin i / sin r = Sin 30 / Sin 19.24 = 0.5 / 0.3295 = 1.517

(b) Frequency always remains constant in case of refraction or reflection.

Velocity of light in air = frequency x wavelength in air

Frequency = (3 x 10^8) / (632.8 x 10^-9) = 4.74 x 10^14 Hz

(c) let the speed of light in solution is v.

refractive index of solution = speed of light in air / speed of light in solution

1.517 = 3 x 10^8 / v

v = 3 x 10^8 / 1.517 = 1.98 x 10^8 m/s

(d) Let the wavelength of light in solution is λs.

refractive index of solution = wavelength in air / wavelength in solution

λs = 632.8 / 1.517 = 417.14 nm