Double Slit, Central Diffraction Maximum

[jegues]

Homework Statement

See figure attached for problem statement as well as my attempt

Homework Equations

The Attempt at a Solution

I don't know where to go from here. Can someone help me get started?

 

[jegues]

Bump still looking for help

 

[ehild]

See:
http://scienceworld.wolfram.com/physics/DiffractionGrating.html

ehild

 

[jegues]

See:
http://scienceworld.wolfram.com/physics/DiffractionGrating.html

ehild

We haven't looked at anything that complicated in my course. There must be an easier way to solving this...

 

[jegues]

Here's my best attempt at reasoning things out.

I'm not getting the right answer, but it's a shot!

 

[ehild]

What have you learned about the diffraction pattern of multiple slits?

There are two patterns: one from the single-slit diffraction, the other from the interference between the rays traversing separate slits. The minima of the diffraction pattern are at sin(θ)=m λ/a where a is the slit width and m =±1, ±2,... You get the interference maxima from two slits d=340μm apart at sin(θ)=n λ/d.

The first minima in the diffraction patter are at the angles where sin(θ_-1)=- λ/a and sin(θ₁)= λ/a. The "distance" between the interference maxima are λ/d. You see five bright lines in the range of the first diffraction maximum. What can be the ratio between a and d?

ehild

 

[jegues]

What have you learned about the diffraction pattern of multiple slits?

There are two patterns: one from the single-slit diffraction, the other from the interference between the rays traversing separate slits. The minima of the diffraction pattern are at sin(θ)=m λ/a where a is the slit width and m =±1, ±2,... You get the interference maxima from two slits d=340μm apart at sin(θ)=n λ/d.

The first minima in the diffraction patter are at the angles where sin(θ_-1)=- λ/a and sin(θ₁)= λ/a. The "distance" between the interference maxima are λ/d. You see five bright lines in the range of the first diffraction maximum. What can be the ratio between a and d?

ehild

Here's my attempt at the ratio between a and d. See figure


Am I doing this correctly?

 

[jegues]

I am still stuck. Can please give me another nudge in the right direction, I haven't given up yet.

 

[ehild]

Read the text of the problem again. It is very difficult to read those very tiny letters but I see (with magnifying glass) something about five bright fringes. And sorry, I can not follow your handwriting. Please type in what you did.

ehild