Diffraction grating of laser light

[Johnahh]

Homework Statement

a narrow beam of laser light (i.e coherent monochromatic light) wavelength 630nm is incident on a grating having 300 lines per mm. a piece of paper is curved 180 degrees beyond the grating. calculate how many spots of red light should be seen

Homework Equations

n$\lambda$=d*sin$\theta$
d = spacing between lines
n = order of angle

The Attempt at a Solution

so there's 300 lines per mm and i want to find out d therefore i did $\frac{1}{300000}$ and got 3.33x10^-6 lines per m
so now i can use n*630x10^-9=3.33x10^-6*sin(90)
this makes
n=$\frac{3.33x10^-6*sin(90)}{630x10^-9}$

this gives me 4.72 which I can round up to 5 and multiply by 2 to get the order for 180 degrees.
so I get an answer of 10 and the books answer is 11.
what am I doing wrong

P.S first time using latex...

 

[mfb]

and got 3.33x10^-6 lines per m

This should be meter per line I think.

You forgot the central spot at an angle of zero.

 

[technician]

check your calculation, I got n to be just greater than 5. As mfb says, you forgot the central max (n = 0)
If n was 4.72 then you would only see 9 spots (including the central max)
You cannot 'round up' the value of n !

 

[Johnahh]

you are correct that should have been meter per line. I knew I must have been forgetting something.
Thankyou

 

[Johnahh]

technician, after seeing your reply I have noticed my calculator is still in radians from my math revision. now i get 5.29 down to 5. Thanks lol