What Determines the Center of a Diffraction Pattern?

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]
I did not understand what is meant by the center of the pattern here.

a) I have $\delta \theta_{hw} = \frac { \lambda }{Nd \cos{\theta }}$

For central maximum $\theta = 0$, so central line has less width than other line. So, the central line is towards left. But, how to decide center of pattern?

b) Since angular half – width is proportional to $\lambda$ , for less $\lambda$ , the half – widths of the line will be less.

 

[lekh2003]

The center of every pattern always has the widest fringe. This is one of the first things you must have learnt. Can you now figure out where is the center?

I'm not too sure about the second question.

 

[Pushoam]

The center of every pattern always has the widest fringe.

How do you get to know this?
If this is true then, the center of the pattern is towards right. Is this correct?

 

[Pushoam]

For central maximum θ=0θ=0 \theta = 0, so central line has less width than other line. So, the central line is towards left. But, how to decide center of pattern?

Center of the pattern is the point where the central maximum of diffraction occurs. If this is true, then since the line corresponding to central maximum has the smallest width, the center of the pattern will be towards left. Is this correct?

 

[lekh2003]

If this is true, then since the line corresponding to central maximum has the smallest width

What? This line will be the thickest since it is the central maximum. Central maximum. You are under an incorrect assumption. A diffraction grating with monochromatic light will definitely have a the maximum at the center. In multi-wavelength light, the fringes are thicker, but the larger fringes approach the center.

 

[Pushoam]

What? This line will be the thickest since it is the central maximum. Central maximum. You are under an incorrect assumption. A diffraction grating with monochromatic light will definitely have a the maximum at the center. In multi-wavelength light, the fringes are thicker, but the larger fringes approach the center.

Why should line corresponding to central maximum be thickest?

Half – angular width of line is given by $\delta \theta_{hw} = \frac { \lambda }{Nd \cos{\theta }}$.

In case of central maximum, $\theta = 0$ , so the angular width of central maximum is the smallest. Hence, the line width of the central maximum line is smallest.

The intensity of the central maximum line should be greatest, why should be thickness be greatest?

 

[lekh2003]

Why should line corresponding to central maximum be thickest?

Half – angular width of line is given by $\delta \theta_{hw} = \frac { \lambda }{Nd \cos{\theta }}$.

In case of central maximum, $\theta = 0$ , so the angular width of central maximum is the smallest. Hence, the line width of the central maximum line is smallest.

The intensity of the central maximum line should be greatest, why should be thickness be greatest?

Maybe this thread will help you: https://www.physicsforums.com/threa...tic-light-vs-white-light.729546/#post-4610077

 

[Pushoam]

The central maximum of each order is shown to have same width in the above picture. For a given order the central maximum has the largest width.

In the question, I have to compare central maximum of each order. And m = 0 corresponds to the center of the pattern.

Could you please show me the equation which says central maximum of m =0 is has the largest width?