# Diffraction - maxima

1. Oct 28, 2010

### shyta

1. The problem statement, all variables and given/known data
Show that the angular locations of the first to fourth secondary maximas are $$\alpha$$ = a sin $$\Theta$$/$$\Lambda$$ = 1.43030 2.45902 3.47089 4.46641 respectively.

a is the slit width = 0.00016m
$$\Lambda$$ wavelength of laser 650nm

2. Relevant equations

I($$\Theta$$) = I0 [sin($$\Pi\alpha$$)/$$\Pi\alpha$$]2

where I0 is the intensity at the central peak

3. The attempt at a solution

I have no idea how to begin..

2. Oct 29, 2010

### sungod

You have an equation for the intensity of the diffraction pattern. The maxima and minima of the function will give the maxima and minima of the diffraction pattern. So, simply differentiate and set to zero. You'll get two factors. One of these gives the minima and the other gives the maxima, or, at least, another equation for the maxima. Solving the "maxima equation" will give the values at which the maxima occur.

3. Oct 31, 2010

### shyta

hi there

after differentiating, i got this equation

2I0 sin($$\pi$$$$\alpha$$)/$$\pi$$^2$$\alpha$$^3 ($$\pi \alpha$$ cos($$\pi\alpha$$) - sin $$\pi\alpha$$ )

i hope this is correct.. anyway i set this to zero and got 2 different sets of eqn.

2I0 sin($$\pi$$$$\alpha$$)/$$\pi$$^2$$\alpha$$^3 = 0

so sin($$\pi$$$$\alpha$$) = 0
$$\alpha$$ = 0,1,2,3,...

and ($$\alpha$$^2 cos($$\pi\alpha$$) - sin $$\pi\alpha$$ ) = 0
$$\pi\alpha$$ = tan ($$\pi\alpha$$)
how do I solve this?

Last edited: Nov 1, 2010
4. Nov 1, 2010

### shyta

sorry the correct maxima eqn should be this.

$$\pi$$$$\alpha$$ = tan ($$\pi$$$$\alpha$$)

how do i solve it?

5. Nov 1, 2010

### sungod

Let me rewrite this as
b = tan(b)

Plot y = b and y = tan(b) on the same plot. Where the two plots intersect are the solutions.