How Is Slit Width Calculated in Single Slit Diffraction?

[SamTsui86]

Homework Statement

A diffraction pattern is produced on a screen 130 cm from a single slit, using monochromatic light of wavelength 460 nm. The distance from the center of the central maximum to the first-order maximum is 2.20 mm. Calculate the slit width. (Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.)

Homework Equations

y1 = L sin (theta) = L (wavelength / a)

The Attempt at a Solution

wavelength = 460 e -9 m
L = .13 m
y = .0022 m
so I found a

.0022 = .13 sin (theta)
sin (theta) = .0169 = (wavelength/ a)

a = .0272 mm

How anyone tell me what I am doing wrong?

 

[Hootenanny]

$$130\;cm \neq 0.13\;m$$

 

[SamTsui86]

oops :) my bad