Find Width of Slit for Diffraction Maxima

[Seigi Yokota]

Homework Statement

A single slit diffracts laser light of wavelength 650 nm onto a screen 2.00 m away. The distance between the two first-order maxima on either side of the central peak is 2.05 mm. How wide is the slit?

Homework Equations

a=width of slit
y=distance from central max to specific spot
L=distance of screen from the slit
λ=wavelength of light
sinΘ≈Θ=y/L
minima occurs at: a*sinΘ=mλ
(found on internet) approximation of maxima occurs at: a*sinΘ=(m+.5)λ

The Attempt at a Solution

L=2m
λ=650*10^-9m
each maxima is the same distance from the central maxima so if the distance between the 2 first order maxima is .00205m then
y=.001025m

a*(.001025/2)=(1.5)(650*10^-9)
I found answer to be 0.001902m (wrong)

just in case I decided to try and see using the minima formula a*(.001025/2)=(650*10^-9)
answer :0.001268m (wrong)

any assistance would be great.

 

[Khashishi]

The maximum of the sinc function is not at m+0.5 . It's close, but not exactly.

 

[Seigi Yokota]

The maximum of the sinc function is not at m+0.5 . It's close, but not exactly.

what equation should I use then?

 

[BvU]

You differentiate the intensity expression...