In summary, the problem involves a green laser with a wavelength of 532 nm being sent through two slits with a separation of 127 μm. The question asks for the total width of the 11 green dots formed when projected onto a screen 1.25 m away from the slits. Using the equations mλ=dsinθ and tanθ = Y/L, the solution involves finding the angle θ and distance Y from m=0 to m=5. The total width of the 11 dots is twice the distance between m=0 and m=5, which is equal to 5.24x10^-2m.
  • #1
Sullo
15
0

Homework Statement


If a green laser is (wavelength = 532nm) sent through two slits with a separation of 127 um, how wide (in total) would the 11 green dots formed be if they were projected onto a screen 1.25m away from the slits?

Refer to this diagram sorry for bad quality: https://imgur.com/a/ACcJYJd
Double Slit.jpg

Homework Equations


mλ=dsinθ
tanθ = Y/L

The Attempt at a Solution


First find θ

sinθ = mλ/d

sinθ = [(5)(5.32x10^-9)] / 1.27x10^-6
sinθ = 2.09x10^-2
θ = 1.2 degrees

second, find distance from m = 0 to m = 5 (Y)
tanθ = Y/L
Y = Ltanθ
Y = 1.25tan(1.2)
Y = 2.61x10^-2m

So therefore, the total distance of the 11 dots will be twice the distance between M=0 and M=5
Total width of 11 dots = (2.61x10^-2) x 2 = 5.24x10^-2m
 

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  • #2
Sullo said:

Homework Statement


If a green laser is (wavelength = 532nm) sent through two slits with a separation of 127 um, how wide (in total) would the 11 green dots formed be if they were projected onto a screen 1.25m away from the slits?

Refer to this diagram sorry for bad quality: https://imgur.com/a/ACcJYJd

Homework Equations


mλ=dsinθ
tanθ = Y/L

The Attempt at a Solution


First find θ

sinθ = mλ/d

sinθ = [(5)(5.32x10^-9
)] / 1.27x10^-6
sinθ = 2.09x10^-2
θ = 1.2 degrees

second, find distance from m = 0 to m = 5 (Y)
tanθ = Y/L
Y = Ltanθ
Y = 1.25tan(1.2)
Y = 2.61x10^-2m

So therefore, the total distance of the 11 dots will be twice the distance between M=0 and M=5
Total width of 11 dots = (2.61x10^-2) x 2 = 5.24x10^-2m
532 nm is 532x10-9m.
And what is the slit separation? 127 μm or 1.27 μm?
 
  • #3
ehild said:
532 nm is 532x10-9m.
And what is the slit separation? 127 μm or 1.27 μm?

127um
 

1. What is Young's double slit experiment?

Young's double slit experiment is a classic experiment in physics that demonstrates the wave-like nature of light. It involves shining a beam of light through two narrow slits and observing the resulting interference pattern on a screen.

2. Why is a green laser used in Young's double slit experiment?

A green laser is used in Young's double slit experiment because it has a specific wavelength of light that is visible to the human eye and is easily distinguishable from other colors. This makes it easier to observe and measure the interference pattern on the screen.

3. How does the interference pattern in Young's double slit experiment change with different colored lasers?

The interference pattern in Young's double slit experiment will change with different colored lasers because each color has a different wavelength. This results in a different spacing between the interference fringes on the screen, which can be observed and measured.

4. What does the interference pattern in Young's double slit experiment tell us about the nature of light?

The interference pattern in Young's double slit experiment tells us that light behaves like a wave, as it exhibits the same interference and diffraction patterns as other wave phenomena. This supports the wave theory of light, which states that light is a form of electromagnetic radiation.

5. How is Young's double slit experiment relevant to modern science?

Young's double slit experiment is still relevant to modern science as it continues to be used to study the properties of light and confirm the wave nature of light. It has also been adapted and applied to other areas of science, such as quantum mechanics and electron diffraction, providing valuable insights into the behavior of particles at the atomic level.

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