Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 4.90m away from the slits.
1. What is the distance Δy_max-max between the first maxima (on the same side of the central maximum) of the two patterns?
2. What is the distance Δy_max-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?
What is your question here? A standard equztion on angles, then a trig triangle to figure distance.
what was your answer? :)
kinda need it.......... assignment is due in 15 minutes....
answer is 9.33×10−2 m
and the answer to the second part??
To find the distance Δy_max-max between the first maxima of the two patterns, we need to calculate the position of the first maxima for each laser separately and then find the difference between them.
1. Calculate the position of the first maxima for laser 1:
The position of the maxima in a double-slit interference pattern can be calculated using the formula:
y = λL / d
where:
y is the distance from the central maximum,
λ is the wavelength of the laser,
L is the distance between the double slits and the screen, and
d is the distance between the slits.
Using the values provided, we have:
λ_1 = d/20,
L = 4.90m, and
d is given.
Substituting these values into the formula, we can calculate the position of the first maxima for laser 1.
y_1 = (d/20) * (4.90m) / d
= (4.90m) / 20
= 0.245m
2. Calculate the position of the first maxima for laser 2:
Using the same formula, but with the wavelength of laser 2 (λ_2 = d/15), we can calculate the position of the first maxima for laser 2.
y_2 = (d/15) * (4.90m) / d
= (4.90m) / 15
≈ 0.327m
3. Calculate the distance Δy_max-max:
Δy_max-max = y_2 - y_1
= 0.327m - 0.245m
≈ 0.082m
Therefore, the distance Δy_max-max between the first maxima of the two patterns is approximately 0.082m.
To find the distance Δy_max-min between the second maximum of laser 1 and the third minimum of laser 2, we can use a similar approach.
1. Calculate the position of the second maximum for laser 1:
Since we already have the position of the first maximum for laser 1 (y_1), we can use the formula for double-slit interference pattern:
y = λL / d
to calculate the position of the second maximum.
For laser 1, we use the same values as before, except now we consider the second maximum:
y_1_max2 = (d/20) * (4.90m) / d
= (4.90m) / 20
= 0.245m
2. Calculate the position of the third minimum for laser 2:
Using the formula for laser 2, we can calculate the position of the third minimum:
y_2_min3 = (d/15) * (4.90m) / d
= (4.90m) / 15
≈ 0.327m
3. Calculate the distance Δy_max-min:
Δy_max-min = y_2_min3 - y_1_max2
= 0.327m - 0.245m
≈ 0.082m
Therefore, the distance Δy_max-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum, is approximately 0.082m.