A laser beam is incident at an angle of 29.4° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.84° to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution (c) Find its frequency in the solution (d) Find its speed in the solution

a) For the ray going into syrup, angle of incidence (i) is 29.4 and angle of refraction (r) is 18.84

Refractive index of syrup = Sin i / Sin r

= Sin 29.4 / Sin 18.84

= 1.51.

b) The wavelength of a light is reduced in a medium by the factor of refractive index so

wavelength in the medium

= Wavelength in air / refractive index of the solution

= 632.8 / 1.51

= 419.07 nm.

The frequency remains unchanged. The frequency in the medium will be same as that in air or vacuum.

Frequency in air = Velocity of light in air / wavelength in light

= 3 x 10⁸ / 632.8 x 10⁻⁹

= 4.74 x 10¹⁴ Hz.

Frequency in the medium is same as that in air.

Velocity in the medium

V = velocity in air / refractive index

= 3 x 10⁸ / 1.51

= 1.98 x 10⁸ m / s