Question

Due to the Doppler effect, waves from an approaching source (moving toward the observer)are observed as having a shorter wavelength than when they were emitted. What colorwould a green star rapidly approaching Earth appear to be if it was obsreved from Earth?

Answer 1

According to the doppler effect,

The value of the frequency of light observed by the observer on the earth when the star is moving towards the earth is defined by,

`\\u^(\prime)=\\u_(green)(1+(u)/(c))`

where u is the velocity of the star with respect to earth.

As the wavelength and the frequency of light are related as,

`\begin{gathered} c=\\u\lambda \\ \\u=(c)/(\lambda) \end{gathered}`

By using this relation, the doppler effect in terms of wavelength become,

`\begin{gathered} (c)/(\lambda^(\prime))=(c)/(\lambda_(green))(1+(u)/(c)) \\ (1)/(\lambda^(\prime))=(1)/(\lambda_(green))(1+(u)/(c)) \\ (1)/(\lambda^(\prime))=(1)/(\lambda_(green))((c+u)/(c)) \\ \lambda^(\prime)=\lambda_(green)((c)/(c+u)) \end{gathered}`

As c+u is greater than c,

This shows that wavelength of the light observed by the observer will be less than the wavelength of green light.

Thus, the light of the star observed by the observer on the earth will be blue shifted.

Hence, the green star approacking towards the earth will appeared to be of blue colour.