Angular Position of 1st Dark Fringe in Two-Slit Interference Pattern?

So, the first dark fringe will be at an angular position of 0.5 degrees. You can use the small angle approximation when calculating the angular position.In summary, to find the angular position of the first dark fringe when a blue laser beam of wavelength 470nm is incident on two narrow slits separated by .2mm, you can use the formula dsin(theta)=(n + 1/2 )(lambda) and the small angle approximation. The first dark fringe will be located at an angular position of 0.5 degrees.
  • #1
NelielSwann
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Homework Statement


A blue laser beam of wavelength 470nm (in air) is incident on two narrow slits separated by .2mm and produces an interference pattern on a screen located 2m away from the two slits.

Find the angular position (in degrees) of the 1st dark fringe. Can you use the small angle approximation?


Homework Equations


dsin(theta)=n(lambda)
tan(theta)= y/L



The Attempt at a Solution


I've searched all over for a formula to find the dark fringes, but all i can find is one for the light ones. the dsin(theta)=n(lambda) is used for the maxima. what formula do i use for the minima/dark fringes?
 
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  • #2
For dark fringes use dsin(theta)=(n + 1/2 )(lambda)
 
  • #3
For two-slit interference, the minima are halfway in between the maxima.
 

1. What is the double slit experiment and how does it relate to dark fringes?

The double slit experiment is a classic experiment in physics that involves shining a beam of light through two parallel slits and observing the resulting interference pattern. This experiment demonstrates the wave-like nature of light and how it can interfere with itself to create bright and dark fringes. The dark fringes are areas where the light waves cancel each other out, resulting in no light being detected.

2. What factors affect the visibility of dark fringes in the double slit experiment?

The visibility of dark fringes in the double slit experiment can be affected by several factors, including the wavelength of the light, the distance between the slits, and the distance between the slits and the screen where the interference pattern is observed. Additionally, the intensity of the light source and the size of the slits can also impact the visibility of the dark fringes.

3. How can the double slit experiment with dark fringes be used to determine the wavelength of light?

The double slit experiment with dark fringes can be used to determine the wavelength of light by measuring the distance between the dark fringes on the interference pattern. This distance, known as the fringe spacing, is directly related to the wavelength of light used in the experiment. By knowing the distance between the slits and the screen, and measuring the fringe spacing, the wavelength of light can be calculated using the formula λ = ds/D, where λ is the wavelength, d is the distance between the slits, and D is the distance between the slits and the screen.

4. Can dark fringes be observed with other types of waves besides light?

Yes, dark fringes can be observed with other types of waves besides light. The double slit experiment has been performed with various types of waves, including sound waves, water waves, and even electrons. In each case, the interference pattern generated by the waves shows regions of constructive and destructive interference, resulting in bright and dark fringes.

5. How has the understanding of dark fringes in the double slit experiment contributed to our understanding of the nature of light?

The understanding of dark fringes in the double slit experiment has contributed to our understanding of the nature of light by demonstrating its wave-like behavior and the concept of interference. This experiment has also led to the development of wave-particle duality, which states that light can exhibit both wave-like and particle-like properties. Additionally, the double slit experiment has been used to study the properties of light, such as its wavelength and speed, and has played a crucial role in the development of quantum mechanics.

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