Alaser 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

Explanation:

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