During the transition of light waves from a vacuum to a certain transparent medium, the wavelength decreased

During the transition of light waves from a vacuum to a certain transparent medium, the wavelength decreased by 1.31 times. What kind of environment is it?

First, we need the refractive index of the medium, which reflects how many times the speed of light in a vacuum is greater than in another medium.

It is found by the formula: n = c / v, where n is the refractive index of the medium, c is the speed of light in vacuum, v is the speed of light in the 2nd medium.

From the condition of the assignment: λ / λ ‘= 1.31, since when passing from medium to medium, the wavelength decreased by 1.31 times. λ is the wavelength in vacuum, λ ‘is the wavelength in the 2nd medium, f is the frequency.

The wavelength in vacuum is found by the formula: λ = c / f,

Wavelength in the 2nd medium according to the formula: λ ‘= v / f,

Therefore: λ / λ ‘= (c / f) / (v / f) = c / v = 1.31;

n = 1.31 Looking at the table of refractive index values, we will see that our environment is ice.