Question

A spaceship from a friendly, extragalactic planet flies toward Earth at 0.201 times the speed of light and shines a powerful laser beam toward Earth to signal its approach. The emitted wavelength of the laser light is 697 nm . Find the light's observed wavelength on Earth.

Answer 1

The wavelength of observed light on earth is 568.5 nm

Step-by-step explanation:

Given that,

Velocity of spaceship
`v= 0.201c`

Wavelength of laser
`\lambda= 697\ nm`

We need to calculate the wavelength of observed light on earth

Using formula of wavelength

`\lambda_(0)=\lambda_(e)*\sqrt{(1-(v)/(c))/(1+(v)/(c))}`

`\lambda_(0)=697*10^(-9)*\sqrt{(1-(0.201 c)/(c))/(1+(0.201c)/(c))}`

`\lambda_(0)=697*10^(-9)*\sqrt{(1-0.201)/(1+0.201)}`

`\lambda=5.685*10^(-7)\ m`

`\lambda=568.5*10^(-9)\ m`

`\lambda=568.5\ nm`

Hence, The wavelength of observed light on earth is 568.5 nm