Calculating Width of Single Slit Diffraction Pattern

[phy112]

Homework Statement

The central bright fringe in a single slit diffraction pattern from light of wavelength 412 nm is 1.9 cm wide on a screen that is 1.05 m from the slit.

How wide is the slit?

Homework Equations

i keep trying the equation .5asintheta=.5wavelength
I can't seem to get the right answer but I am sure its easy

The Attempt at a Solution

 

[Doc Al]

Express sinθ in terms of pattern position and distance to screen. (Use a small angle approximation.)

 

[phy112]

is it the eq. tantheta=h/D?

 

[Doc Al]

is it the eq. tantheta=h/D?

Yes, and for small angles tanθ ≈ sinθ.

 

[phy112]

do you use h=1.9 cm and D=1.05m?

 

[Doc Al]

do you use h=1.9 cm and D=1.05m?

Not exactly. Note that in the diffraction equation, "h" is measured from the central maximum.

Also, when you wrote ".5asintheta=.5wavelength" why do you have .5 in there?

Read this: http://hyperphysics.phy-astr.gsu.edu/HBASE/PHYOPT/sinslit.html"