A distant star emiftied a light with wavelength lambda 486

A distant star emiftied a light with wavelength lambda = 486 mm when it was 52 Mpc away from ut, when the light reached us, the distance has expanded to 53 Mpc what is the light\'s new wavelength? Answer:

Solution

let the star is moving at speed V away from earth.

So velocity of light in earths frame is,

C\'=(C-V)/(1-C*V/C^2)=(C-V)/(1-V/C)=C

V=1Mpc/(52Mpc/C)=C/52

So the frequency observed by the earth will be smaller and the wavelength will be greater.

The new frequency is,

f\'=f*sqrt[(1-V/C)/(1+V/C)]

so,V/C=1/52

l\'=l*sqrt[(1+V/C)/(1-V/C)]=495.4 nm

The wavelength is 495.4 nm