Question

A laser beam with vacuum wavelength 582 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. Take θ1 to be 60°. Recall that the index of refraction of air is 1 and Lucite is 1.50. (a) Find the speed of the light in Lucite.. m/s (b) Find the frequency of the light in Lucite.. Hz (c) Find the wavelength of the light in Lucite. nm

Answer 1

(a)

The index of refraction in Lucite is

n = c/v

Here, speed of light in vacuum is c and speed of light in Lucite is v.

From the above equation, the speed of light in Lucite is

v = c / n

speed of light, c = 3 * 10⁸  and n = 1.50

v = c / n

   = 3 x 10⁸ m/s / 1.50

v = 2 x 10⁸ m/s

Therefore, the speed of light in Lucite is 2 x 10⁸ m/s.

(b)

Frequency of light remains constant when it travels from vacuum to Lucite.

The frequency of light in Lucite is equal to the frequency of light in vacuum.

Now, the frequency of light in vacuum is

f = c /

= (3 * 10⁸) / 582 nm

= (3 * 10⁸) / 582 * 10^-9 m

= 5.15 * 10¹⁴ Hz

(c)

The index of refraction is also the ratio of the wavelength of light in vacuum to the wavelength of light in Lucite.

n = / _L

where, _L is the wavelength of light in Lucite.

From the above equation, the wavelength of light in Lucite is

_L = / n

= (582 * 10^-9) / 1.50

= 388 * 10^-9 m

= 388 nm