# Optical Physics; Light Entering an Atmosphere

• Carusun
In summary, the question involves a light ray entering an atmosphere with an increasing index of refraction, and the task is to find the time it takes for the light to travel a distance of 20.0 km. Using the relationship between velocity and refractive index, the answer is found to be 6.683x10^-5s. The use of integration is necessary to solve the problem, and the final answer is obtained by setting n=1+.005t/T, where T is the time it takes for the light to travel the given distance.
Carusun
[SOLVED] Optical Physics; Light Entering an Atmosphere

Homework Statement
Quoted word for word from the question sheet:

A light ray enters the atmosphere of a planet and descends vertically 20.0 km to the surface.
The index of refraction where the light enters the atmosphere is 1.000, and it increases linearly towards the surface where it has a value of 1.005.
a) How long does it take the ray to traverse this path?
b) Compare this to the time it takes in the absence of an atmosphere.

The attempt at a solution
Right, I know (or at least, I'm fairly sure that I do) the final answer, just not how to properly obtain it.
I know that the velocity of light through a medium is related to the refractive index by v=c/n, and I know that the time it takes for the light to travel a certain distance is given by t=s/v.

By working out the change in n per metre, and plugging it into a program I whipped up in MatLAB, I got a time of 6.683x10^-5s, which seems reasonable compared to the answer of 6.67*10^-5 I got for part b)

So I'm just stumped on how to get the answer without doing it the long way. Something tells me to use integration, but I've tried that with t=(s*n)/c and I end up with an answer 200 times too small.

Many thanks in advance for any help rendered, I'm sure that once it's explained I'll be kicking myself :P

Let n=1+.005t/T.
$$20=\int_0^T(c/n)dt$$.
Solve for T.

Many thanks! Got the answer now :)

I knew that integrating was involved, I just couldn't make that last leap :D

## 1. How does light interact with the atmosphere?

Light interacts with the atmosphere in several ways. When light enters the atmosphere, it can be scattered, absorbed, or transmitted. Scattering occurs when light particles are deflected in different directions by particles in the atmosphere, such as dust, water vapor, or gases. Absorption happens when the light particles are absorbed by particles in the atmosphere, causing them to lose energy. Transmission occurs when light passes through the atmosphere without being scattered or absorbed.

## 2. Why does the sky appear blue during the day?

The sky appears blue during the day because of a phenomenon called Rayleigh scattering. This is when shorter, blue wavelengths of light are scattered more easily by particles in the atmosphere compared to longer, red wavelengths. So, the blue light is scattered in all directions, giving the sky its blue appearance.

## 3. How does the Earth's atmosphere affect the speed of light?

The Earth's atmosphere can affect the speed of light in two ways. Firstly, the refractive index of the atmosphere is slightly higher than that of a vacuum, meaning light travels slightly slower in the atmosphere. Secondly, the density and composition of the atmosphere can cause light to bend or slow down as it passes through, affecting its overall speed.

## 4. What is the difference between visible light and infrared light?

Visible light and infrared light are both part of the electromagnetic spectrum, but they have different wavelengths and energy levels. Visible light has a shorter wavelength and higher energy compared to infrared light. This means that visible light is visible to the human eye, while infrared light is invisible but can be detected by special cameras or sensors.

## 5. How does the atmosphere affect the color of the sun during sunrise and sunset?

The atmosphere can affect the color of the sun during sunrise and sunset because of the angle at which sunlight enters the atmosphere. During these times, the light has to pass through more of the atmosphere, causing more scattering and absorption to occur. This results in longer, redder wavelengths being more visible, giving the sun a warm, orange or red hue.

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