A laser beam with vacuum wavelength 6328 nm is incident from

A laser beam with vacuum wavelength 632.8 nm is incident from air onto a block of Lucite as shown in the figure below. The line of sight of the photograph is perpendicular to the plane in which the light moves. (Assume that the incidence angle is 55°, and the refraction angle is 33°.)

(a) Find the speed of the light in the Lucite.
m/s

(b) Find the frequency of the light in the Lucite.
Hz

(c) Find the wavelength of the light in the Lucite.
nm

Solution

angle of incidence , i = 55 degree

angle of refraction , r = 33 degree

a)

let the refractive index of lucite is n

Using snell\'s law

n * sin(r) = sin(i)

n * sin(33) = sin(55)

n = 0.819/0.544 = 1.50551

speed of light in Lucite = c/n

speed of light in Lucite = 3 *10^8/1.50551

speed of light in Lucite = 2 *10^8 m/s

b)

frequency of light is f

as the frequency is not dependent on the medium

frequency * 632.8 *10^-9 = 3 *10^8

frequency = 4.74 *10^14 Hz

the frequency of the light in the Lucite is 4.74 *10^14 Hz

c)

wavelength in Lucite = wavelength in vaccum/n

wavelength in Lucite = 632.8/1.50551

wavelength in Lucite = 421.86 nm