Double slit - find wavelength

In summary, using the given data from the double slit experiment, the wavelength can be found using the equation xn/L=(n-0.5)(\lambda/d) or xm/L=(m)(\lambda/d). The distance between the 5th and 1st maxima is provided, along with the angle to the 8th maximum, which can be used to calculate the wavelength as 610nm.
  • #1
quicksilver123
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Homework Statement



The following data was obtained via the double slit experiment:

angle to the eighth maximum = 1.12 degrees
distance from slits to screen = 302cm = 3.02m
distance from first to fifth mimum = 2.95cm
distance between slits = 0.00025m

find the wavelength.

Homework Equations



supposed to use this equation to find wavelength:

xn/L=(n-0.5)([itex]\lambda[/itex]/d)
or
xm/L=(m)([itex]\lambda[/itex]/d)

The Attempt at a Solution



problem is, there's no given value for xm or xn

how can i get this value?

(oh, and i specifically have to use the equation listed above)
 
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  • #2
##x_m## is the distance off axis of the mth maximum, numbering the central bright spot as ##m=0##. You can immediately write the distance between the Mth and mth maxima as ##x_M-x_m=(M-m)L\lambda/d##. A little manipulation gets you ##\lambda=d (x_M-x_m)/L (M-m)##. You provided the distance between the M=5 and m=1 maxima. Plugging that and your other data in gets you ##\lambda=610##nm.

You also gave the angle to the 8th maximum, which tells us that the distance from the axis to the 8th maximum is 3.02 sin(1.12)=0.059m. Plugging that in with M=8, m=0 also yields 610nm.
 

1. What is the double slit experiment?

The double slit experiment is a classic physics experiment that demonstrates the wave-like behavior of particles. It involves shining a beam of particles (such as photons or electrons) through two slits and observing the resulting interference pattern on a screen.

2. How does the double slit experiment determine wavelength?

The double slit experiment uses the interference pattern created by the particles passing through two slits to calculate the wavelength. The distance between the interference fringes on the screen is directly proportional to the wavelength of the particles.

3. What is the relationship between the distance between the slits and the wavelength?

The distance between the slits and the wavelength have an inverse relationship in the double slit experiment. This means that as the distance between the slits increases, the wavelength of the particles decreases.

4. Can the double slit experiment be used to find the wavelength of any type of particle?

Yes, the double slit experiment can be used to find the wavelength of any type of particle that exhibits wave-like behavior. This includes photons, electrons, and even larger particles like atoms and molecules.

5. Are there any limitations to using the double slit experiment to find wavelength?

While the double slit experiment is a powerful tool for determining wavelength, it does have some limitations. For example, the particles must be small enough to exhibit wave-like behavior and the experimental setup must be carefully controlled to avoid outside interference.

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