Wavelength, Frequency, and Speed of Light in Different Media

In summary, the problem involves a monochromatic laser beam traveling through a piece of glass with a thickness L and an index of refraction n. The wavelength of the light is L/10 and its frequency is f. The question asks for the time it takes for a pulse of light to travel through the glass. The solution involves drawing a diagram and using the equation t = Ln/c where c is the speed of light and n is the index of refraction. The frequency of the light can also be used to solve the problem.
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Homework Statement


A beam of light from a monochromatic laser shines into a piece of glass. The glass has a thickness L and an index of refraction n . The wavelength of the laser light in vacuum is L/10 and its frequency is f. In this problem, the constant should not appear in any of your answers.

How long does it take for a short pulse of the light to travel from one end of the glass to the other?

Homework Equations



None of any significance i can think of that will help us here

The Attempt at a Solution



t = (L/10)(f)(n)
 
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  • #2
Okay, the best thing to do is to draw a diagram, I always find this helps to visualize the
problem. You know that the time the light is inside the media is simply t = s/v. Now s = L
so t = L/v. And the speed of the light inside the glass is of course c/n. Hence t = Ln/c. I wasn't sure what you meant by "the constant should not appear in any of your answers" if you mean that the frequency of the light, which is constant whatever media it is in, then that's your answer. Otherwise, you can simply substitute to get the answer in the form that you need.
You can also use c = l*f (l=wavelength, f=frequency) will also be of use.

Matt.
 
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1. What is the relationship between wavelength, frequency, and speed of light in different media?

Wavelength, frequency, and speed of light are all related through the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This means that as the wavelength decreases, the frequency increases and vice versa. The speed of light also varies depending on the medium it is traveling through.

2. How does the speed of light change in different media?

The speed of light can change in different media due to the different densities and refractive indices of the materials. In general, light travels slower in denser materials such as water and glass, but faster in less dense materials such as air. The speed of light also changes depending on the wavelength of the light.

3. What is the relationship between the speed of light and the index of refraction?

The index of refraction is a measure of how much a material can bend light. It is directly related to the speed of light in that material, with a higher index of refraction resulting in a slower speed of light. This is because the higher the index of refraction, the more the material can slow down and bend the light as it passes through it.

4. How do wavelength and frequency affect the properties of light in different media?

The wavelength and frequency of light determine its energy and how it interacts with different materials. In general, shorter wavelengths (such as gamma rays and X-rays) have higher energy and can penetrate through materials more easily, while longer wavelengths (such as radio waves) have lower energy and are more easily absorbed or reflected by materials.

5. Why is the speed of light different in a vacuum compared to other media?

In a vacuum, there are no particles to slow down or interact with the light, so it can travel at its maximum speed of approximately 299,792,458 meters per second. In other media, the light interacts with particles and is slowed down, resulting in a lower speed. This is also why the speed of light in a vacuum is often used as a universal constant in physics equations.

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