Diffraction grating that gives max intensity

[toforfiltum]

Homework Statement

Homework Equations

dsinθ=nλ
IαA²

The Attempt at a Solution

I chose D because I thought that D gives the max intensity since the amplitudes superimpose over a smaller area. But the answer is C. I can't see why.

 

[soarce]

From diffracting grating one gets 1st order beam (undeflected), 2nd order deflected beam, 3rd order deflected beam and so on. This would rule out the answer A and D. The intensity decerases with the intensity order, in the picture we have no information about the beam intensities represented by arrows, however we have information about the deflection angle, what's the difference between C and D?

 

[toforfiltum]

From diffracting grating one gets 1st order beam (undeflected), 2nd order deflected beam, 3rd order deflected beam and so on. This would rule out the answer A and D. The intensity decerases with the intensity order, in the picture we have no information about the beam intensities represented by arrows, however we have information about the deflection angle, what's the difference between C and D?

Why is D ruled out? It has a 1st order beam unlike A.

 

[soarce]

I have made a mistake in my previous post: the undeflected beam should be 0th order.

I was thinking that the answer D limits the number of diffraction orders to one.

LE: Think on the diffraction orders and their diffraction angles, use the formula you have written.

 

[toforfiltum]

I have made a mistake in my previous post: the undeflected beam should be 0th order.

I was thinking that the answer D limits the number of diffraction orders to one.

LE: Think on the diffraction orders and their diffraction angles, use the formula you have written.

I thought that the intensity of the waves falls off as the order increases?

 

[soarce]

The arrows shows the direction of diffracted beams, from the picture I can't distinguish any difference in arrows width (if any). I assume that each arrow stands for a diffraction order.

Did you reach any conclusion examining the diffraction angles of B, C and D figures ?

 

[toforfiltum]

The arrows shows the direction of diffracted beams, from the picture I can't distinguish any difference in arrows width (if any). I assume that each arrow stands for a diffraction order.

Did you reach any conclusion examining the diffraction angles of B, C and D figures ?

For C and D, angle for 1st order in C is larger than in D. The only logical thing I can think of is that that beam of light from C is directed away from the centre, which means centre is less bright. I just don't understand the answer.

 

[soarce]

From $d\sin\theta_n = n \lambda$ one can calculate the diffraction angles for each order, n=0,1,2,3 etc Use some particular ratio $\lambda/d$, e.g. 1, 0.5, 0.3, 0.25, to see how the diffraction angles relates to the diffractoin orders. You can write your results here.

 

[toforfiltum]

From $d\sin\theta_n = n \lambda$ one can calculate the diffraction angles for each order, n=0,1,2,3 etc Use some particular ratio $\lambda/d$, e.g. 1, 0.5, 0.3, 0.25, to see how the diffraction angles relates to the diffractoin orders. You can write your results here.

Oh I see why now. If the order is only until 1, then the angle of light would be at 90°, which is impossible to reach screen. Am I right?

 

[soarce]

Right! The ratio $\lambda/d$ gives a cut-off in the diffraction orders. Now compare $\theta_n$ and $\theta_{n+1}$, where $n=0,1,2,3...$

 

[toforfiltum]

Right! The ratio $\lambda/d$ gives a cut-off in the diffraction orders. Now compare $\theta_n$ and $\theta_{n+1}$, where $n=0,1,2,3...$

The angles from 0th order increase gradually, so B can't be right because it he increase in 1st angle order is greater than increase in 2nd angle order.

 

[soarce]

Right! What happens in D?

 

[toforfiltum]

Right! What happens in D?

The first order beam of light should be at 90° to 0th order?

 

[soarce]

In figure D we have only on diffraction order, the second order would have a diffraction angle greater than 90°. Does this situation fit with the relationship between $\theta_n$ and $\theta_{n+1}$ which we established before?

 

[toforfiltum]

In figure D we have only on diffraction order, the second order would have a diffraction angle greater than 90°. Does this situation fit with the relationship between $\theta_n$ and $\theta_{n+1}$ which we established before?

No, but isn't figure D wrong in the first place? Like I said in post #9?

 

[soarce]

Post #9 refers to the second order.
In figure D we have only the 1st order. Following your remark in post #11, what angle must have the 1st order so that the 2nd one goes beyond 90°?

 

[toforfiltum]

Post #9 refers to the second order.
In figure D we have only the 1st order. Following your remark in post #11, what angle must have the 1st order so that the 2nd one goes beyond 90°?

45°?

 

[soarce]

45°?

That's correct, but in figure D we see a 1st order angle much smaller than 45 degrees.

 

[toforfiltum]

That's correct, but in figure D we see a 1st order angle much smaller than 45 degrees.

Ok, thanks a lot!

 

[TSny]

45°?

If the second order is at 90^o, at what angle is the first order? Use dsinθ = nλ to find out.