Find the angular width of the central maximum.

[bsmm11]

Homework Statement

A single slit of width 1.50 * 10^-6m is illuminated with light of wavelength 500.0 nm. Find the angular width of the central maximum.

Homework Equations

θ = λ / b

The Attempt at a Solution

b = 1.50 * 10^-6m
λ = 5.000 * 10^-7
θ = λ / b = 0.333 = 19.1°

But the answer is 38.9°.

All my calculation of diffraction on single slit is off-target. It seems there is a fundamental point that I am missing. Please help.

 

[Dadface]

You have found the angular position,measured from the centre,of the pattern.There are two such minima,one on each side of the central maxima.

 

[bsmm11]

OK.. so what I need is 2Θ, right? Then I got 38.2, and this is a bit off from 38.9. Where did this difference come from?

 

[Dadface]

I calculated it to be 38.9.The equation is:
sin theta=lambda/d.
Did you take theta to be in radians?If so that is a good approximation but only for very small angles.

 

[Emilyjoint]

I had a similar problem and was given this link.
http://www.calctool.org/CALC/phys/optics/fNA
It is a great link and solved my problem with units

 

[bsmm11]

Now I can solve the problems. Thanks everyone! :D

p.s. Emily, the link is not valid. Could you give me a right one? I can solve the problems, but still I want to check it out.