Determine the wavelength of light in glass if the wavelength in vacuum is 0.5 μm.

Determine the wavelength of light in glass if the wavelength in vacuum is 0.5 μm. Light falls from a vacuum onto glass at an angle of 60 ° and refracts at an angle of 30 °.

Snell’s Law:

sin a / sin b = n2 / n1 = v1 / v2,

where a is the angle of incidence of the beam,

b – angle of refraction,

n1 is the refractive index of the first medium

n2 is the refractive index of the second medium.

v1, v2 – the speed of light in the first medium and the second medium.

Substitute the values:

sin 60⁰ / sin 30⁰ = s / vc,

where c and vc are the speeds of light in vacuum and glass.

vc * sin 60⁰ = c * sin 30⁰;

vc = c * (1/2) / (√3 / 2) = c / √3.

The frequency of light f does not change during the transition:

f = s / λ,

where λ is the wavelength in vacuum.

Glass wavelength:

λс = v2 / f = (s / √3) / (s / λ) = λ / √3 = 0.5 μm / √3 = 0.29 μm.

Answer: 0.29 microns.