A spaceship approaches Earth at a speed of 0.42c. A light on the front of the ship appears red (wavelength 650 nm) to passengers on the ship. What (a) wavelength and (b) color (blue, green, or yellow) would it appear to an observer on Earth?

Short Answer

Expert verified

(a) The wavelength of light for observer on Earth is 415nm.

(b) The color of light for observer on Earth is blue.

Step by step solution

01

Identification of given data

The wavelength of light is λo=650nm.

The speed of spaceship is v=0.42c

The wavelength of light for observer on Earth is calculated by using the formula for Doppler effect in light and color of light is decided by wavelength of light.

02

Determination of wavelength of light for observer on Earth

(a)

The wavelength of light for observer on Earth is given as

λ=λo1+vc1-vc

Here, c is the speed of light and its value is 3×108ms.

Substitute all the values in the above equation.

λ=615mm1+0.42cc1-0.42ccλ=415nm

Therefore, the wavelength of light for observer on Earth is 415nm.

λ=λo1+vc1-vc

03

Identification for color by wavelength

(b)

The wavelength of the light falls between wavelength of blue and green on visible spectrum but it is nearer to blue color wavelength so color of light for observer on Earth is blue.

Therefore, the colour of light for observer on Earth is blue.

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