A light wave has a 670 nm wavelength in air.

vegetars8t

vegetars8t

Answered question

2021-12-09

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. 
a. What is the light speed in this substance?
b. What is the light’s frequency in the solid?

Answer & Explanation

maul124uk

maul124uk

Beginner2021-12-10Added 35 answers

Step 1
Index of refrection:
n=cv
n index of refraction of an optical material.
c speed of light in space,
v speed of light in the material
Light always travels more slowly in a material than in vacuum, so the value of n in anything other than vacuum is always greater than unity. Note that: the index of refraction depends on each material
Apply: in most cases we need the speed of light in a specific medium, so we use the index of refraction for this medium to get the speed of light in this medium,
Step 2
Weve speed for a periodic wave:
v=λT=λf
The wave advances a distance of one wavelength λ during one period T, so the wave speed is given by:
v=λT, f=1T
v=λT=λ f
v the speed of wave,
f the frequency of the wave,
T The periodic time,
λ wavelength of the wave.
This equation is applied to any kind of periodic waves. The wave of a string will explain it more:
For a periodic wave, the shape of the string at any instant is a repeating pattern. The wavelength of the wave is the distance from one crest to another, or from one trough to the next, or from any point to the corresponding point on the next repetition of the wave shape. The wave pattern travels with constant speed and advances a distance of one wavelength in a time interval of one period T.
Apply: in most problems we use the equation directly to get one of the variables by knowing the other variables such as the wave speed and wavelength. Sometimes we need to get the frequency by knowing the time period by using the relation above or getting the speed using the frequency and the wavelength.
Step 3
a) v=c=3×108ms
v=c=λf
fair=fsolid=f=cλ
=3×108ms670×109m=4478×1014Hz
The frequency is the dame in air and glass as is same source
vsolid=fsolidλsolid
=(4.478×1014Hz)(420×109m)=1.88×108ms
Step 4
b) fair=fsolid=f=cλ
=3×108ms670×109m=4.478×1014Hz
amarantha41

amarantha41

Beginner2021-12-11Added 38 answers

Step 1 
Only the wavelength and speed of a beam of light change as it travels through different media, not its frequency. The experimental speed of light in air is: 
3×108ms 
Therefore, the frequency of this beam of light is: 
v=fλ
where v is speed, f is frequency, and λ is the wavelength. The frequency thus is: 
3×108670×109=4.48×1014Hz 
The frequency will remain the same in the solid medium 
The speed will then become: 4.48×1014×420×109=1.88×108 meters per second

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