# Single slit diffraction

1. Dec 9, 2007

### neelakash

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.]

2. Dec 9, 2007

### siddharth

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

3. Dec 9, 2007

### neelakash

t is transmission co-efficient

4. Dec 9, 2007

5. Dec 9, 2007

### neelakash

Ok

Any better argument?

6. Dec 9, 2007

7. Dec 9, 2007

### neelakash

Exactly,I was talking of this derivation.