(a) How fast must you be approaching a red traffic (λ= 675 nm) for it to appear yellow (λ= 575 n

step 1 In the first part of this problem, we are going to calculate the speed of the person for which t

(a) How fast must you be approaching a red traffic (λ= 675...

(a) How fast must you be approaching a red traffic ($\lambda=$ 675 nm) for it to appear yellow ($\lambda=$ 575 nm)? Express your answer in terms of the speed of light. (b) If you used this as a reason not to get a ticket for running a red light, how much of a fine would you get for speeding? Assume that the fine is $1.00 for each kilometer per hour that your speed exceeds the posted limit of 90 km/h.

(a) How fast must you be approaching a red traffic ($\lambda=$ 675 nm) for it to appear yellow ($\lambda=$ 575 nm)? Express your answer in terms of the speed of
light. (b) If you used this as a reason not to get a ticket for running a red light, how much of a fine would you get for speeding? Assume that the fine is $1.00 for each kilometer per hour that
your speed exceeds the posted limit of 90 km/h.

Key Concepts

Relativistic Doppler Effect

The relativistic Doppler effect describes how the observed wavelength of light changes when there is relative motion between the source and the observer at speeds significant compared to the speed of light. It uses a formula that accounts for time dilation and relates the emitted wavelength to the observed wavelength, allowing one to determine the velocity at which a light source must be moving for its color (wavelength) to shift from one value to another.

Wavelength and Color Perception

The color we perceive from light is directly linked to its wavelength. In the visible spectrum, different wavelengths correspond to different colors (for example, red vs. yellow). A Doppler shift can move the emitted wavelength of light into a different region of the visible spectrum, thereby changing its perceived color.

Unit Conversion in High-Speed Contexts

When working with speeds given as a fraction of the speed of light, it is often necessary to convert these speeds into common units such as meters per second or kilometers per hour. This conversion is essential when linking theoretical relativistic results to practical contexts, such as determining fines based on speed limits.

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