Answer:
The wavelength of observed light on earth is 568.5 nm
Explanation:
Given that,
Velocity of spaceship [tex]v= 0.201c[/tex]
Wavelength of laser [tex]\lambda= 697\ nm[/tex]
We need to calculate the wavelength of observed light on earth
Using formula of wavelength
[tex]\lambda_{0}=\lambda_{e}\times\sqrt{\dfrac{1-\dfrac{v}{c}}{1+\dfrac{v}{c}}}[/tex]
[tex]\lambda_{0}=697\times10^{-9}\times\sqrt{\dfrac{1-\dfrac{0.201 c}{c}}{1+\dfrac{0.201c}{c}}}[/tex]
[tex]\lambda_{0}=697\times10^{-9}\times\sqrt{\dfrac{1-0.201}{1+0.201}}[/tex]
[tex]\lambda=5.685\times10^{-7}\ m[/tex]
[tex]\lambda=568.5\times10^{-9}\ m[/tex]
[tex]\lambda=568.5\ nm[/tex]
Hence, The wavelength of observed light on earth is 568.5 nm
