Question

A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship
emits light of wavelength λ = 4500Å which appears blue to a passenger on the
spaceship. What colour would the light appear to a person on earth?

Answer 1

Answer on Question #74931-Physics-Other

A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship emits light of wavelength $\lambda = 4500\,\text{\AA}$ which appears blue to a passenger on the spaceship. What colour would the light appear to a person on earth?

Solution

$$\lambda = 4500\,\text{\AA}$$ $$v = 0.3c$$ $$\lambda' = \lambda \frac{1 + \frac{v}{c}}{\sqrt{1 - \frac{v^2}{c^2}}}$$ $$\lambda' = 4500 \frac{1 + 0.3}{\sqrt{1 - 0.3^2}} = 6132.5\,\text{\AA}.$$

Thus, the new color of light is orange.

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