What is the dependence on w of intensity in single slit diffraction?

[neelakash]

Homework Statement

Interesting Problem...

monochromatic light of wavelength $$\lambda$$ falls on a slit and is transmitted as

t=1 for 0<x<(d/2)
t=-1 for (-d/2)<x<0
t=0 otherwise...

Define $$\ w$$=$$\ k(d/2)$$$$\sin$$$$\theta$$...[most possibly,if I can exactly remember...]

Now what should be the dependence on w of Intensity $$\I(\theta)$$?

It was a multiple choice question and a number of options were given...

(A) $$\frac{sin^2 \omega}{\omega^2}$$

(B) $$\frac{sin^2 \frac{\omega}{2}}{\omega^2}$$

(C) $$\frac{cos^2 \omega}{\omega^2}$$

(D) $$\frac{sin\omega}{\omega}$$

Homework Equations

The Attempt at a Solution

(B) seems plausible to me as it considers w/2...Note that in this particular problem,the phasor amplitudes are different about the centre.If you take the geometrical point of view,the phasor vectors will be a bit different than they are shown normally.
[I do not know which classical book uses the geometrical phasor derivation...I saw it in Resnick Halliday Krane's fifth volume.]

 

[siddharth]

What is 't'? I'm not familiar with this notation.

 

[neelakash]

t is transmission co-efficient

 

[Doc Al]

(B) seems plausible to me as it considers w/2...

Answer (B) is correct.

 

[neelakash]

Ok

Any better argument?

 

[Doc Al]

I don't know of any clever argument, other than reprising the standard phasor derivation. Here's one version: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html#c1"

 

[neelakash]

Exactly,I was talking of this derivation.