Number of lines/cm for the grating

[physicsstoodent]

The problem is:

Three, and only three, bright fringes can be seen on either side of the central maximum when a grating is illuminated with light ( = 520 nm). What is the maximum number of lines/cm for the grating?

Here is what i know / did:

since there are three fringes, m = 3

since they are bright fringes, it's constructive interference so (m lambda)

we know that d sin(theta) = (m lambda)

so, d sin(theta) = (3 * 5.20 E-7 meters)

we know that the highest displacement has to occur when theta is 90 degrees. So, sin of 90 gives you 1.

d sin(90) = (3 * 5.2 E -7); D = 1.56 E-6 meters <- This is the slit separation, I am stuck at this point.

 

[physicsstoodent]

Never Mind

I figured it out

Nmax = 1 / D min

since d = 1.54 E-6 m = 1.5 E -4 cm

1 / 1.54 E -4 cm = 6410 lines/cm.