Young's Double Slit Experiment - Slit Separation Calculation

In summary, to calculate the slit separation, you can use the equation d = (m * wavelength * D) / y, where d represents the slit separation, m is the order of the diffraction pattern, wavelength is the wavelength of the light, D is the distance from the slit to the screen, and y is the distance between the center and side order. By plugging in the given values of wavelength (650 nm), m (1), D (37.5 cm), and y (0.7 cm), you can calculate the slit separation to be 0.0348 mm. However, this value may not match the theoretical value of 0.25 mm, indicating a possible error in the experiment or a missing component
  • #1
MrBob22
2
0

Homework Statement



Calculate the slit separation (d) given that:

Wavelength = 650 nm (Plugged in 6.5*10^-7 m)
m = 1 (plugged in 1)
Distance to screen (D) = 37.5 cm (plugged in 0.375m)
Distance between centre to side order (y) = 0.7 cm (pluged in 0.007m)

Homework Equations



We were only given one equation in our lab manual (the same equation they gave us for a single slit, slit width problem...except instead of d they had a there to represent slit width)

d = (m*Wavelength*D)/y

where d is the slit separation

The Attempt at a Solution



I plugged in the numbers and I produced a solution equal to 0.0348 mm. (I made sure to convert to meters before plugging into the equation and then converted back to milimetres by multiplying by 1000)

What ails me is that the theoretical, or given slit separation is 0.25mm. This makes my relative error aproximately 88% and I am positive I did not do the experiment that poorly. Surprisingly though, the answer produced is VERY similar to the given SLIT WIDTH (0.04mm).

Now I checked this a million times and I think I may be stuck in a rut of not seeing something that is supremely obvious but is making me get the wrong answer. Or the person who designed my lab did not supply me with a proper equation to solve this problem.

Any help is appreciated.
 
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  • #2
Distance between centre to side order (y) = 0.7 cm (pluged in 0.007m)

Can you show, how did you get the above value?
 
  • #3
Well, all this data comes from an experiment. Basically what happened was we had a laser shoot through a slit. It diffracted and left a pattern of lights on a white sheet of paper. What we did then was mark each of these lights with a pencil (up to m=2). We then measured the distance between the two marked lines (m1 on the left to m1 on the right). To get the value of y we had to divide this number in 2 (to get the distance to the center).

What was measured for 2y (the distance between two of these ticks) was 1.4cm.

So I did:

1.4cm/2 = 0.7cm
0.7cm/100 = 0.007m
 
Last edited:

1. What is the concept behind Young's Double Slit Experiment?

The Young's Double Slit Experiment is a classic experiment in optics and wave interference that demonstrates the wave-like nature of light. It involves a light source, two parallel slits, and a screen where the light is projected. The light passing through the slits diffracts and creates an interference pattern on the screen, showing that light behaves like a wave.

2. How is the slit separation calculated in Young's Double Slit Experiment?

The slit separation, also known as the slit spacing, is the distance between the two parallel slits. It is calculated by dividing the distance between the center of the screen and the central bright spot in the interference pattern by the distance from the screen to the slits. This calculation can be represented by the equation d = λL/D, where d is the slit separation, λ is the wavelength of the light, L is the distance from the slits to the screen, and D is the distance between the slits and the light source.

3. What is the significance of the slit separation in Young's Double Slit Experiment?

The slit separation plays a crucial role in determining the characteristics of the interference pattern in Young's Double Slit Experiment. A smaller slit separation results in a wider interference pattern, while a larger slit separation leads to a narrower pattern. Additionally, the slit separation affects the spacing between the bright and dark fringes in the interference pattern.

4. How does changing the slit separation affect the interference pattern in Young's Double Slit Experiment?

As mentioned, the slit separation has a direct impact on the interference pattern in Young's Double Slit Experiment. Changing the slit separation changes the spacing between the bright and dark fringes, as well as the overall shape of the pattern. A smaller slit separation leads to a wider pattern with more fringes, while a larger slit separation results in a narrower pattern with fewer fringes.

5. How is the slit separation related to the wavelength of light in Young's Double Slit Experiment?

The slit separation is directly proportional to the wavelength of light used in Young's Double Slit Experiment. This means that as the wavelength increases, the slit separation also increases. This relationship can be seen in the equation d = λL/D, where a larger value for λ will result in a larger value for d. This relationship is essential in understanding the behavior of light as a wave and in analyzing the results of the experiment.

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