Question

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm.

Answer 1

Answer: speed of light in solid = 1.88 * 10^8 m/s

Frequency is constant

Explanation: The relationship between the velocity of light wave and wavelength is given by the formulae below

V = fλ

During refraction, the frequency of light is constant, thus we have that

V = kλ which implies that velocity is proportional to wavelength.

Hence, we have that

v1/ λ1 = v2/ λ2

Where v1 = velocity of light in air = 3 * 10^8 m/s

v2 = velocity of sound in solid

λ1 = wavelength of light in air = 670nm

λ2 = wavelength of light in solid = 420nm

By making v2 subject of formulae, we have that

v2 = v1 * λ2/ λ1

v2 = 3 * 10^8 * 420nm/ 670nm

v2 = 3 * 10^8 * 0.6268

v2 = 1.88 * 10 ^8 m/s

b)

During refraction the frequency of light wave is constant this is because light consist of photons which has energy. it energy needs to be constant and for energy (E=hf) to be constant, frequency would be constant too.