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Physics Lesson 12.7.2 - The Doppler Effect in Light Waves

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Welcome to our Physics lesson on The Doppler Effect in Light Waves, this is the second lesson of our suite of physics lessons covering the topic of The Doppler Effect, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

The Doppler Effect in Light Waves

The Doppler Effect in light waves occurs in a similar way as in sound waves. The only difference is the introduction of a new factor, β = v/c in the formula of the new light frequency, where v is the relative speed of the moving object to the source and c is the speed of light in vacuum (c = 3 × 108 m/s). There are two possible cases in this regard:

1. When source and detector are separating from each other

The formula of frequency for the Doppler Effect in this case is:

f = f0 × √1 - β/1 + β

The new frequency will be lower than the original one. Therefore, a phenomenon known as "red-shift" does occur. It means the detected light frequency will shift towards the red part of visible light spectrum, as red light represents the part of the visible light spectrum with the lowest frequency.

2. When source and detector are approaching each other

In this case, we have:

f = f0 × √1 + β/1 - β

Obviously, the new frequency is higher than the original one. Therefore, a phenomenon known as "blue-shift" does occur. It means the detected light frequency will shift towards the blue part of visible light spectrum as blue light represents a part of the visible light spectrum with high frequency (it should have been violet, but violet belongs to the family of blue light).

Example 4

A star emits an apparently blue light of frequency 7.5 × 1014 Hz but when measured by using special techniques, it results that the original frequency of the light emitted by this star is 5.45 × 1014 Hz (green light). What is happening to the star if we take the Earth as a frame of reference?

Solution 4

Since the original light is green but it appears blue, there is a blue shift in the light frequency. This means the star is approaching the Earth.

To calculate the approaching speed v, we must therefore use the formula

f = f0 × √1 + β/1 - β

Thus, we have

7.5 × 1014 = 5.45 × 1014 × √1 + β/1 - β
1.376 = √1 + β/1 - β
1.894 = 1 + β/1 - β
1.894-1.894 × β = 1 + β
0.894 = 2.894 × β
β = 0.3089

Since

β = v/c

we obtain for the approaching speed of the star:

0.3089 = v/3×108
v = 0.3089 × 3 × 108
= 9.267 × 107 m/s
= 92 670 km/s

Remark! We can also use the wavelength instead of frequencies in all the above formulae. We must only transform them in the proper way in order to fit the theory.

You have reached the end of Physics lesson 12.7.2 The Doppler Effect in Light Waves. There are 2 lessons in this physics tutorial covering The Doppler Effect, you can access all the lessons from this tutorial below.

More The Doppler Effect Lessons and Learning Resources

Optics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
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Notes
Revision
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12.7The Doppler Effect
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
12.7.1The Doppler Effect in Sound Waves
12.7.2The Doppler Effect in Light Waves

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