# Diffraction maxima

1. Apr 12, 2015

### Seigi Yokota

1. The problem statement, all variables and given/known data
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?

2. Relevant 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

3. 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)

any assistance would be great.

2. Apr 12, 2015

### Khashishi

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

3. Apr 12, 2015

### Seigi Yokota

what equation should I use then?

4. Apr 12, 2015

### BvU

You differentiate the intensity expression...