Question

A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship
emits light of wavelength 4500 Å(angstrom) 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 # 74065, Physics Mechanics - Relativity:

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

Solution: We know,

$$\lambda' = \lambda \frac{1 + \frac{v}{c}}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} \quad \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots$$

Where,

- $\lambda' =$ wavelength of light with respect to earth

- $\lambda =$ wavelength of light with respect to spaceship = 4500 Å

- $v =$ velocity of spaceship = 0.3 C (C = speed of light)

Put the value of $\lambda$ and $v$ in equation (1), we get,

$$\lambda' = 4500 \times \frac{1 + 0.3}{\sqrt{1 - (0.3)^2}} = 6157.89 \text{ Å (approx.)}$$

This wavelength corresponds to orange light.

Answer: Orange colour will appear to a person on the earth.

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