Calculating the Speed of a Galaxy Using Diffraction Grating and Doppler Effect

[HaLAA]

Homework Statement

Taking light collected by the telescope and shine it through a diffraction grating with a 765.5 lines/mm. Using the filter that just the brightest Helium II line. you cast the diffraction grating's diffracted pattern on a screen is 22.000cm away and there are 3 dots, m=-1, m=0 amd m=1. the distances between m=-1 and m=1 is 10.7314.

find the speed of the galaxy moving away from us?

Homework Equations

d sin theta =m lambda
y_m=Ltan lambda
Doppler effect

The Attempt at a Solution

At first, I think I need to find the angel by using: y_m=Ltan lambda
then I have: 0.22 tan theta _1 =0.107314/2 → theta=47.3972 degrees

Since I have the angel, I can find the wavelength of the light by using: d sin theta =m lambda
then I have: 1mm/765.5 sin (47.3972)= 1*lambda → lambda = 962 nm

I get stuck at this step, can anyone give me a hit to get the answer?

Thanks

 

[TSny]

At first, I think I need to find the angel by using: y_m=Ltan lambda
then I have: 0.22 tan theta _1 =0.107314/2 → theta=47.3972 degrees

You set this up correctly, but your answer for the angle θ is not correct.

Think about how to use the Doppler effect to get the speed of the galaxy.

 

[HaLAA]

You set this up correctly, but your answer for the angle θ is not correct.

Think about how to use the Doppler effect to get the speed of the galaxy.

θ=13.7ο,
λ=309nm, this is the initial wavelength.

the equation of the Doppler effect is λ=λ'√(1+v_s/c)/(1-v_s/c)

309nm is λ' , I dont't see how to get λ with the information I have.

 

[TSny]

What is the normal wavelength for the brightest He II line?

 

[HaLAA]

What is the normal wavelength for the brightest He II line?

I don't know, the question doesn't give me any information about that

 

[gneill]

I don't know, the question doesn't give me any information about that

Your text or notes will likely contain the value. If not it can be looked up online. The NIST site should have a table.