please help with physics problem

Question

A 530 lines/mm diffraction grating is illuminated by light of wavelength 540 nm. How many bright fringes are seen on a 3.5- m -wide screen located 2.2 m behind the grating?

Please help

Answer 1

dsin(θ_n) = nλ are the bright fringes on one side of the central spotbright fringe. The answer will be 2n+1 if n is the number of bright fringes to one side of the central bright spot.

We are not solving for all possible bright spots which would entail solving for the largest n so that θ is the greatest angle less than 90°.

In this case we must use the equation y_n = Ltanθ_n (Normally the equation nλ/d = y_n/L is only used for the first or 2nd fringe (small θ)) L is distance to the screen.

Process:

1) θ_n = tan^-1(screen width/2 /L) (Remember it's one-sided analysis)

2) n = (d/λ)sin(θ_n) (Note d = (1/530) mm and λ = 540 nm → put both in meters)

3) Truncate n to next integer value. Answer is 2n+1

Please consider a tutor. Take care.