How Many Bright Fringes Appear on the Screen in a Diffraction Experiment?

[bigsaucy]

A diffraction grating with 600 lines/mm is illuminated with light of wavelength 500nm. A very wide viewing screen is 2.0m behind the grating.

b.) How many bright fringes can be seen on the screen.

MY ATTEMPT:

i worked out the angular separation between bright fringes to be 0.305 rad (i know this is right because i got the answer to part a right). So then the screen has a total angle of 180 degrees or pi rad. therefore i reasoned that the number of fringes is pi rad/0.305 rad. But since there won't be any bright fringe at 0 rad or pi rad, the final solution must be pi (rad/0.305 rad - 2)

Is this reasoning correct or am I completely off? (Note, the answer is 7 fringes)

 

[Doc Al]

Hint: What's the highest order fringe visible on the screen?

 

[bigsaucy]

Yeah... still not hitting any switches, sorry, lol.
How are we meant to find the number of orders?

 

[Doc Al]

What equation tells you the angle that a bright fringe makes?

 

[bigsaucy]

d sin theta = m lambda?

 

[Doc Al]

d sin theta = m lambda?

Exactly. Use that to find the greatest value of m that can appear on screen.

 

[bigsaucy]

I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?

 

[Doc Al]

I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?

Ah, but theta is not an unknown. What's the largest angle that a fringe could make and still be visible on the screen? (For all practical purposes.)