Laser light of wavelength 785 nm in air travels from air (index of refraction = 1) into a glass block (index of refraction = 1.5). The frequency of the light does not change when the light enters the glass. How does the wavelength of the light change, if at all, when the light enters the glass, and what reasoning supports this claim?
Question
Laser light of wavelength 785 nm in air travels from air (index of refraction = 1) into a glass block (index of refraction = 1.5). The frequency of the light does not change when the light enters the glass. How does the wavelength of the light change, if at all, when the light enters the glass, and what reasoning supports this claim?
Solution
The wavelength of the light changes when it enters the glass. This is due to the change in speed of light when it travels from one medium to another.
The speed of light in a medium is given by the equation v = c/n, where c is the speed of light in vacuum and n is the index of refraction of the medium.
When light travels from air into glass, its speed decreases because the index of refraction of glass (1.5) is greater than that of air (1).
The frequency of light does not change when it enters a different medium. This is because frequency is determined by the source of the light and is not affected by the medium it travels through.
The wavelength of light, however, does change when it enters a different medium. This is because wavelength is inversely proportional to the speed of light in the medium.
The wavelength of light in a medium is given by the equation λ = λ0/n, where λ0 is the wavelength of light in vacuum and n is the index of refraction of the medium.
So, when light of wavelength 785 nm in air enters a glass block, its wavelength becomes 785 nm / 1.5 = 523 nm.
Therefore, the wavelength of the light decreases when it enters the glass.
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