# Homework Help: Diffraction grating question

1. Jan 19, 2009

### seanmcgowan

1. The problem statement, all variables and given/known data
Monochromatic light shines on the surface of a diffraction grating with 5.3x10^3 lines/cm. The first order maximum is observed at an angle of 17 (degrees). Find the wavelength.

a) 420nm c) 530nm
b) 520nm d) 550nm

2. Relevant equations
d(sin $$\Theta$$)=m$$\lambda$$

d= 5.3x10^lines/cm=5.3x10^3 lines/m

$$\Theta$$=17

m (the order maximum)= 1
3. The attempt at a solution
I rearranged the problem so it looked like this: $$\lambda$$=(d$$\Theta$$)/m

Since m=1, I dropped it and only worked with the numerator.

The distance between the slits is 1/53 metres so the full equation looks like this: (1/53)(sin17)= $$\lambda$$

(1/53)(.29)=$$\lambda$$
.0054716981=$$\lambda$$

Just by looking at this answer its easy to see its wrong, but why? I followed the equation, so whats up? Any help would be appreciated.

2. Jan 19, 2009