Double Slit Problem: Laser Wavelength & Intensity

[whiskey04]

Two lasers are shining on a double slit, with slit separation . Laser 1 has a wavelength of , whereas laser 2 has a wavelength of . The lasers produce separate interference patterns on a screen a distance 5.80 away from the slits.

Part A
Which laser has its first maximum closer to the central maximum?

Part B
What is the distance between the first maxima (on the same side of the central maximum) of the two patterns?
Express your answer in meters.

Part C
What is the distance between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?
Express your answer in meters.

Not sure where to start ...

currently working with wavelength = (Y*D)/(mR)

 

[muppet]

Have you tried to use LaTeX or something there? You appear to be missing your wavelengths.

 

[Ophelia_S2]

if you are using the textbook: "physics for scientists and engineers" second edition by KNIGHT, you should check out page 675 there are two formulas that is help for. I will list them below in case you are using another texbook.
First one: y_m(y subscrip m) = [m*(lambda)*L]/d where m can be interger.-> position of bright fringes (maximum
second one: y'_m(y' sbscrop m) = [(m+1/2)*(lambda)*L]/d where m can be interger.-> position of dark fringes (minimum)

To help you approach the question, you should compare the change in y by formula one list above. where for laser one, lambda = d/20 ,and laser two, lambda = d/15.
just plug the number in and calculate, the one with lower is closer to central maximum.
(use 1 for m for both, since 0 is central maximum)

part B: use the calculation above to help you solve this one out, subtract both.(watch the signs, keep it positive)

Part C: similar like Part A calculation, where you should be careful with the "m" you use.
For maximum count from 1 because 0 is central max, thus second maximum of l aser 1 use m=2. For minimum count from 0, since there is actully no central min. so the third minimum of laser 2 is still m=2. and then just plug in the number and calculate. keep the result positive.

If you have any further question just take a look of the textbook, or you can post it and i will tried to answer.

If there is anything incorrect people find from my message please that me know..thanks

 

[Ophelia_S2]

Have you tried to use LaTeX or something there? You appear to be missing your wavelengths.

i think it's the question from mastering physics..but i could be wrong.. the wavelengths for laser 1 is d/20 and laser 2 is d/15..

 

[paranormal]

where Y= distance between slits, D= distance to screen, m= order of maximum, R= distance between maxima

As a scientist, my response to this content would be as follows:

Part A: Based on the given information, we can determine that laser 1 has a smaller wavelength than laser 2. This means that laser 1 will have a larger angle of diffraction and therefore, its first maximum will be closer to the central maximum compared to laser 2. Therefore, laser 1 has its first maximum closer to the central maximum.

Part B: Using the equation for the distance between maxima, we can calculate the distance between the first maxima of the two patterns. Plugging in the given values, we get:

λ1 = 600 nm = 6.00 x 10^-7 m
λ2 = 800 nm = 8.00 x 10^-7 m
Y = distance between slits = ?
D = distance to screen = 5.80 m
m = 1 (since we are considering the first maximum)
R = distance between maxima = ?

Using the given equation, we can rearrange it to solve for Y:

Y = (mR*λ)/(D)

For laser 1:
Y1 = (1*R*6.00 x 10^-7 m)/(5.80 m) = 1.03 x 10^-6 m

For laser 2:
Y2 = (1*R*8.00 x 10^-7 m)/(5.80 m) = 1.38 x 10^-6 m

Therefore, the distance between the first maxima of the two patterns is:
Y2 - Y1 = (1.38 x 10^-6 m) - (1.03 x 10^-6 m) = 0.35 x 10^-6 m = 3.5 x 10^-7 m

Part C: To calculate the distance between the second maximum of laser 1 and the third minimum of laser 2, we can use the same equation as in Part B, but with different values for m and R.

For laser 1:
m = 2 (since we are considering the second maximum)
R = 2R1 (since we are looking at the distance between the second maximum and the central maximum)

For laser 2:
m = 3 (since we are considering the third