Maxima of Diffraction Grating with 300 Lines/mm and Wavelength of 450 nm

[Viviana]

Homework Statement

Light of wavelength 450 nm is incident normally on a grating with 300 lines per millimeter. How many orders of diffraction maxima can be obtained?

Homework Equations

d sin(theta) = n(lambda)

The Attempt at a Solution

300 lines per millimeter is 3.33 x 10^-6. And 450 nm should be 4.5 x 10^ -7 m.
This is my equation:
3.33 x 10^-6 sin 90 = n (4.5 x 10^ -7)
I get n= 7.4 = 7
The correct answer is 15. But i just can't get this answer. =( Can someone please guide me?

 

[ehild]

What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild

 

[Viviana]

Does that mean there are two maxima for each order?

 

[Viviana]

What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild

Maxima are at both sides. But i still don't know how to get values of m.

 

[Viviana]

Can you please give some more hints

 

[ehild]

m is integer, including negative numbers and zero. So the farthest maxima are either at 90°or -90°.

ehild