Brain buster: A laser sends red light of wavelength 650 nm from air into water in a swimming pool. The index of refraction of the water is 1.33.
(a) What wavelength will the light have in the
water?
(b) What colour would light of this wavelength appear if it were in air?
(c) Why does a swimmer under the water see the light as red?
index of refraction = c/v=λ(vac)/λ(substance)
λ(water) =λ(air)/n=650 nm/1.33=489 nm.
This is the wavelength of violet light
The swimmer sees the red-orange color since our eyes detect the frequency of the light
To answer these questions, we need to understand how light behaves when it passes from one medium to another with a different refractive index.
(a) To find the wavelength of light in water, we can use the formula:
wavelength(water) = wavelength(air) / refractive index(water)
Given that the wavelength of light in air is 650 nm and the refractive index of water is 1.33, we can calculate:
wavelength(water) = 650 nm / 1.33
wavelength(water) ≈ 488.72 nm
So, the wavelength of light in water will be approximately 488.72 nm.
(b) To determine the color of light in air, we should understand that different wavelengths of light correspond to different colors. Here's a rough breakdown:
- Red light: wavelengths around 650-700 nm
- Orange light: wavelengths around 590-650 nm
- Yellow light: wavelengths around 570-590 nm
- Green light: wavelengths around 495-570 nm
- Blue light: wavelengths around 450-495 nm
- Violet light: wavelengths around 380-450 nm
Since the wavelength of light in air is 650 nm, it falls within the range of red light. Therefore, the light would appear red in air.
(c) When a swimmer is under water, the light from the laser goes through a medium transition from air to water. As it enters the water, its wavelength changes due to the different refractive index of water. In this case, the red light with a longer wavelength is less affected by the refraction compared to other colors in the visible spectrum.
Water has a higher refractive index than air, which causes the red light to bend less. This means that the red light remains closer to its original direction as it passes through the water. Consequently, the swimmer perceives the light as red because the majority of the other colors, which have shorter wavelengths, are refracted and scattered away, leaving mostly the red light to be seen.