# Diffraction grating problems

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)

## Answers and Replies

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

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

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

d sin theta = m lambda?

Doc Al
Mentor
d sin theta = m lambda?
Exactly. Use that to find the greatest value of m that can appear on screen.

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
Mentor
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.)