Question

A source emits monochromatic light of wavelength 495 nm in air. when the light passes through a liquid, its wavelength reduces to 434 nm what is the liquid's index of refraction?

a. 1.14
b. 1.49
c. 2.03
d. 1.26
e. 1.33

Answer 1

By definition, the refractive index is
n = c/v
where c = 3 x 10⁸ m/s, the speed of light in vacuum
v = the speed of light in the medium (the liquid).

The frequency of the light source is
f = (3 x 10⁸ m/s)/(495 x 10⁻⁹ m) = 6.0606 x 10¹⁴ Hz

Because the wavelength in the liquid is 434 nm = 434 x 10⁻⁹ m,
v = (6.0606 x 10¹⁴ 1/s)*(434 x 10⁻⁹ m) = 2.6303 x 10⁸ m/s

The refractive index is (3 x 10⁸)/(2.6303 x 10⁸) = 1.1406

Answer: a. 1.14