Why Is My Calculation of Slit Width Using Light Diffraction Incorrect?

[mustang1988]

1. When blue light of wavelength 450 nm falls on a single slit, the first dark bands on either side of center are separated by 51.5°. Determine the width of the slit.




2. sin$$\theta$$=$$\lambda$$/w



3. w=450e-9/sin(51.5)=5.75x10-7
I tried this but it said it was wrong, if anyone could help that would be great.

 

[rl.bhat]

In the problem the given angle is the separation dark bands on either side.
So θ = 51.5/2 degrees.