Double slit experiment

[Joker88]

51.In a double-slit experiment using a single light source passing through two slits, what is observed at a point on a luminescing screen that is 3 1/6 λ from the upper slit and 4 2/3 λ from the lower slit, as shown in the diagram below?

A. A bright spot
B. A light spot
C. A dim spot
D. A dark spot

The explanation doesnt completely makes sense to me. I got the answer right but i dont think i have the complete idea. It seems like they diffract through but their distances make it so they create a dark spot. I'm not sure how theyre destructive though. It seems like there is more to it ! The correct answer is D.

D is the best answer. The distance of the point on the luminescing screen from the two slits differs by one-and-a-half wavelengths. The waves start in phase when they leave their respective slits, but because they travel different distances, they may or may not be in phase when they meet at the screen. The half-wavelength portion of the difference in their two distances is key, because that defines the two waves as being out of phase at the point where they intersect at the screen. When out of phase, the waves undergo destructive interference, producing a node. When dealing with the interference of light, a node presents itself as a dark spot. The best answer is D.

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[MD Odyssey]

51The explanation doesnt completely makes sense to me. I got the answer right but i dont think i have the complete idea. It seems like they diffract through but their distances make it so they create a dark spot. I'm not sure how theyre destructive though. It seems like there is more to it ! The correct answer is D.

Diffraction and interference are two related, but different quantities. This particular problem deals with interference. Are you asking about the physics behind what is creating the pattern on the screen? I'm not sure that I understand your question.

 

[whiteshadodw]

when i first learned the double slit experiment i had NO idea what was going on, this was because i had a weak understand of mechanical waves and phase. then i learned mechanical waves, phase, and constructive and destructive interference before i learned the double slit experiment again. lo and behold. it all made sense.

i suggest you go over phase, waves, and constructive/destructive intereference.

but just to add some insight into the question. what happens if you play a sound from two speakers separated by some distance and the speakers are in phase? in phase, meaning as the sounds come out from the speaker their wave functions look the same at any given time.

at some distances a microphone will pick up higher intensity of sound, and some distances it will pick up no sound. that's constructive and destructive interference. if the path difference from the two speakers to the microphone differs by any integer wavelength, then you get constructive interference, and if the path differs by (n+1/2)*wavelength, then you get destructive interference.

 

[Labminion]

I might be thinking about this the wrong way, but don't the two waves differ by 1 1/6 wavelengths, not 1.5? 4 2/3wavelengths (14/3 = 28/6) - 3 1/6 wavelengths (19/6)= 7/6 wavelengths. Right?

 

[MT Headed]

28 - 19 = 9

But the fast way to answer this in your head is to realize that whole wavelengths don't matter. 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2
Half a wavelength... destructive interference.

 

[bullsfan1986]

I might be thinking about this the wrong way, but don't the two waves differ by 1 1/6 wavelengths, not 1.5? 4 2/3wavelengths (14/3 = 28/6) - 3 1/6 wavelengths (19/6)= 7/6 wavelengths. Right?

Not sure how you're getting 7/6. Should be 9/6=3/2=1.5..Like MTHead said, when they're asking about constructive/destructive interference in a wave of the same wavelength travelling in the same medium, the 1/2 signifies a completely dark spot on the projection screen (or 2 waves 180 degrees out of phase).

 

[Hexon]

Not sure how you're getting 7/6. Should be 9/6=3/2=1.5..Like MTHead said, when they're asking about constructive/destructive interference in a wave of the same wavelength travelling in the same medium, the 1/2 signifies a completely dark spot on the projection screen (or 2 waves 180 degrees out of phase).

so to be in phase, what would the values have to be?😛

 

[bullsfan1986]

so to be in phase, what would the values have to be?😛

Any positive integer. Obviously, 2 waves can also be partially in phase or out of phase as well. For example, a spot produced by 2 waves separated by 90 (pi/2) degrees wouldn't be completely in phase nor would it be completely dark, you would see a dim spot. Understanding a sine wave is critical to understanding problems such as this one.

 

[muhali3]

didn't read the above responses.

but the way I remember this is...

"the path length difference must be a multiple of the wavelength for constructive interference to occur"

in math, this means. d sin theta = m lambda

for destructive interference, you need to be exactly half-way between spots of constructive interference.

 

[Labminion]

Not sure how you're getting 7/6. Should be 9/6=3/2=1.5..Like MTHead said, when they're asking about constructive/destructive interference in a wave of the same wavelength travelling in the same medium, the 1/2 signifies a completely dark spot on the projection screen (or 2 waves 180 degrees out of phase).

I'm not sure how I was getting 7/6, either. This morning, I am getting 9/6. Apparently, the real problem here is that I cannot subtract. I wonder if that will be an issue on the MCAT? 😳

 

[Joker88]

in what situatin would they be in phase or constructive? 1/2 wavelength means theyre destructive so would 1 wavelength (for example) a part be constructive?

 

[bullsfan1986]

in what situatin would they be in phase or constructive? 1/2 wavelength means theyre destructive so would 1 wavelength (for example) a part be constructive?

Yup.