A source at rest emits light of wavelength 500 nm.When it is moving at 0.90c toward an observer, the observer detects light of wavelength:
A)26 nm
B)115 nm
C)500 nm
D)2200 nm
E)9500 nm

Question

Quizplus · Accepted Answer

This problem involves the concept of Doppler effect, where the wavelength of light (or any electromagnetic radiation) measured by an observer depends on the relative motion between the source and observer. If the source is moving towards the observer, the wavelength is compressed (shifted to shorter wavelengths), while if the source is moving away from the observer, the wavelength is stretched (shifted to longer wavelengths). The mathematical formula for this shift is given by:

delta(lambda)/lambda = v/c

where delta(lambda) is the change in wavelength, lambda is the original wavelength, v is the relative velocity between the source and observer, and c is the speed of light.

In this case, the original wavelength lambda is 500 nm, and the relative velocity v is 0.90c (where c = 3.00 x 10^8 m/s). Plugging in these values, we get:

delta(lambda) = lambda * v/c = 500 nm * 0.90c / (3.00 x 10^8 m/s) = 15 nm

Therefore, the observer detects light of wavelength lambda + delta(lambda) = 500 nm + 15 nm = 515 nm. However, the question asks us to choose the nearest answer, which is B) 115 nm. This is because the answer choices are given in nanometers (nm), which is a common unit for measuring wavelengths of light, while we used meters per second in our calculation. To convert 515 nm to meters, we multiply by 10^-9, which gives us:

515 nm * (1 m / 10^9 nm) = 5.15 x 10^-7 m

This wavelength corresponds to green light, which is slightly shifted towards blue due to the Doppler effect. The choice B) 115 nm is too far off, and can be ruled out immediately. Choices A) 26 nm, C) 500 nm, D) 2200 nm, and E) 9500 nm are also incorrect, as they represent extreme shifts that are not possible for a source of visible light moving at relativistic speeds.

A Source at Rest Emits Light of Wavelength 500 Nm