Single-slit diffraction and small angle approximation

[konto77]

Homework Statement

Light of wavelength 587.5 nm illuminates a single 0.75 mm wide slit. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85 mm from the central maximum? (b) Calculate the width of the central maximum.
Use the small angle approximation.

lambda = 587.5 nm
y=0.85 mm
a=0.75 mm

Homework Equations

y=L*lambda/a

The Attempt at a Solution

I easily found part a to be L = 0.0109 m. But i am having trouble finding out part b.

I tried 2*0.0109 m = .0218 but i don't know if that's right since i don't have the answer.




Any help is appreciated.

 

[kuruman]

The central maximum of the diffraction pattern from the slit subtends an angle $\Delta \theta =\dfrac{\lambda}{d}$ where $d$ is the slit width. In the small angle approximation, the width of the maximum on the screen is $w=L~\Delta \theta=\dfrac{\lambda~L}{d}.$