Calculating the Distance Between Interference Maxima: Yellow Light

In summary, the conversation discusses calculating the distance between the first and second maximum on a screen from a double slit experiment. The relevant equations for this calculation are the tangent of theta1 and theta2, which can be found in a textbook on double slit experiments.
  • #1
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Homework Statement



a)Yellow light Lambda= 589nm falls on a double slit. The distance between two slits is d=0.5 mm the width of each slit is a=100 micrometer. A screen showing the interference pattern is located 4 m behind the slits.



Homework Equations



What is the distance between the first and the second maximum on the screen ?


The Attempt at a Solution



To calculate the distance

tan theta1 = X1 / L
tan theta2 = X2/ L

X2 - X1 = is the answer ?

Is this right ? If it is , how can i calculate theta1 and theta2 ?
Thanks
 
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  • #2
Where your textbook discusses the double slit there should be an equation, either for intensity as a function of angle OR the angles of the maxima (1st, 2nd, etc.)
 
  • #3
for your question! To calculate the distance between the first and second maximum on the screen, you can use the equation:

Δx = λL/d

Where:
Δx = distance between maxima (in meters)
λ = wavelength of light (in meters)
L = distance from slits to screen (in meters)
d = distance between slits (in meters)

In this case, we can convert the given values to meters:
λ = 589nm = 589 x 10^-9 m
d = 0.5 mm = 0.5 x 10^-3 m
L = 4 m

Plugging these values into the equation, we get:
Δx = (589 x 10^-9 m)(4 m) / (0.5 x 10^-3 m) = 471.2 x 10^-6 m = 0.4712 mm

So, the distance between the first and second maximum on the screen is 0.4712 mm.

To calculate theta1 and theta2, you can use the equations:
tanθ1 = X1/L
tanθ2 = X2/L
Where:
θ1 and θ2 are the angles at which the maxima occur (in radians)
X1 and X2 are the distances from the center of the screen to the first and second maxima, respectively (in meters)

Using the value of Δx that we calculated above, we can find X1 and X2:
X1 = 0.4712 mm / 2 = 0.2356 mm = 0.2356 x 10^-3 m
X2 = 0.4712 mm + 0.4712 mm = 0.9424 mm = 0.9424 x 10^-3 m

Now, we can plug these values into the equations to find theta1 and theta2:
tanθ1 = (0.2356 x 10^-3 m) / (4 m) = 5.89 x 10^-5
θ1 = tan^-1(5.89 x 10^-5) = 5.89 x 10^-5 radians

tanθ2 = (0.9424 x 10^-3 m) / (4 m) = 2.36 x 10^-4
θ2 = tan^-1(2.36 x 10^-4
 

1. What is the formula for calculating the distance between interference maxima for yellow light?

The formula is d = λL/d, where d represents the distance between interference maxima, λ represents the wavelength of the yellow light, and L represents the distance between the two slits.

2. How do I determine the wavelength of the yellow light?

You can determine the wavelength by using a diffraction grating or a double-slit experiment and measuring the distance between the interference maxima.

3. Can I use this formula for calculating the distance between interference maxima for other colors of light?

Yes, you can use this formula for any color of light as long as you know the wavelength of the light.

4. Is this formula applicable to all types of interference patterns?

Yes, this formula can be used for both Young's double-slit interference and diffraction grating interference patterns.

5. How accurate is this formula for calculating the distance between interference maxima?

This formula is considered to be very accurate, but it may have some limitations when applied to real-life situations due to factors such as experimental error and the assumption of ideal conditions.

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