A ray of light crosses a boundary between two transparent materials. The medium the ray enters has a larger index of refraction. Which of the following statements are true? Check all that apply. Check all that apply. The wavelength of the light decreases as it enters into the medium with the greater index of refraction. The frequency of the light remains constant as it transitions between materials. The speed of the light remains constant as it transitions between materials. The speed of the light increases as it enters the medium with the greater index of refraction. The frequency of the light decreases as it enters into the medium with the greater index of refraction. The wavelength of the light remains constant as it transitions between materials.

The refraction index of a material is given by the formula n=c/v, where c is the speed of light in vacuum and v the speed of light in the material. If a ray of light crosses a boundary between two transparent materials and the medium the ray enters has a larger index of refraction it means that in this new medium the speed of light is smaller than on the other one, and then its wavelength is also reduced since f must remain the same (and [tex]\lambda=v/f[/tex]), otherwise there is a discontinuity on number of vibrations per second, which cannot happen. So we know that:

1) The wavelength of the light decreases as it enters into the medium with the greater index of refraction. True.

2) The frequency of the light remains constant as it transitions between materials. True.

3) The speed of the light remains constant as it transitions between materials. False.

4) The speed of the light increases as it enters the medium with the greater index of refraction. False.

5) The frequency of the light decreases as it enters into the medium with the greater index of refraction. False.

6) The wavelength of the light remains constant as it transitions between materials. False.

oladayoademosu oladayoademosu · Answer 2 · 2022-03-27T00:59:13+01:00

The statements that are true are statement 1 and statement 2

Refractive index

Since refractive index n = c/v where

c = speed of light in less dense medium and
v = speed of light in more dense medium.

Speed of ray of light

Now, when light moves from a material with small index of refraction to a material with large index of refraction, its speed decreases since the number of wavefronts decrease.

Frequency of ray of light

Also, as the ray of light moves from the material with small index of refraction to a material with large index of refraction, its frequency, f is constant.

Wavelength of ray of light

Since its wavelength, λ = v/f where v = speed of light in medium and f = frequency. Since f is constant, λ ∝ v.

Since its speed decreases, so its wavelength also decreases as it, travels into the material with larger refractive index.

So, the statements that are true are

1. The wavelength of the light decreases as it enters into the medium with the greater index of refraction.

2. The frequency of the light remains constant as it transitions between materials.

So, the statements that are true are statement 1 and statement 2

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