What is the Relation Between Distance and Angle in Double Slit Interference?

In summary: The central maximum resides at the normal (or at the centre). Where should the first maximum occur then? Can you somehow approximately relate this distance to the angle you need?The angle is given in the equation as ##\beta=\frac{\lambda D}{d}##.
  • #1
youmei0426
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Homework Statement


question (iii)
upload_2018-12-28_11-31-1.png

2. Homework Equations
D=sd/λ (where D is the distance from slit to screen, s is the distance to the central maxima, and d is the slit separation)[/B]

The Attempt at a Solution


I plugged the values s=0.3*10^(-3), d=4.5*10^(-3) and λ=633*10^(-9), and got the answer 2.13m. However, the answer stays that I need to multiply this value by 2, and I don't know why as the formula doesn't say so. Thanks in advance![/B]
 

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  • #2
Hello youmei, :welcome:

youmei0426 said:
I don't know why as the formula doesn't say so
What exactly is the formula saying (what is it for ? ) And what does the exercise ask ?
 
  • #3
The formula ##\beta=\frac{\lambda D}{d}## denotes the distance of separation between two adjacent maxima (or minima). But you are given the distance between a maximum & the adjacent minimum.
Can you figure it now?
 
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  • #4
PKM said:
The formula ##\beta=\frac{\lambda D}{d}## denotes the distance of separation between two adjacent maxima (or minima). But you are given the distance between a maximum & the adjacent minimum.
Can you figure it now?
thanks a lot!
 
  • #5
PKM said:
The formula ##\beta=\frac{\lambda D}{d}## denotes the distance of separation between two adjacent maxima (or minima). But you are given the distance between a maximum & the adjacent minimum.
Can you figure it now?
I came across another similar problem regarding diffraction grating, and there the diffraction angle is from the normal to the first maximum. So I am a bit confused as to what exactly is the angle in the formula? Thanks!
 
  • #6
youmei0426 said:
I came across another similar problem regarding diffraction grating, and there the diffraction angle is from the normal to the first maximum. So I am a bit confused as to what exactly is the angle in the formula? Thanks!
The central maximum resides at the normal (or at the centre). Where should the first maximum occur then? Can you somehow approximately relate this distance to the angle you need?
 
Last edited:

1. What is double slit interference?

Double slit interference is a phenomenon that occurs when a wave, such as light, passes through two narrow slits and produces a pattern of light and dark fringes on a screen behind the slits. This is due to the interference of the waves from the two slits, causing some areas to have constructive interference (bright fringes) and others to have destructive interference (dark fringes).

2. What is the significance of double slit interference?

Double slit interference is significant because it provides evidence for the wave nature of light. It also demonstrates the concept of interference, which is a fundamental principle in wave mechanics. Additionally, double slit interference is used in many technologies, such as diffraction gratings and interferometers, to control and manipulate light waves.

3. How does the distance between the slits affect the interference pattern?

The distance between the slits, known as the slit separation, directly affects the interference pattern. As the slit separation decreases, the fringes become wider and more spread out, and the distance between the bright fringes increases. As the slit separation increases, the fringes become narrower and closer together, and the distance between the bright fringes decreases.

4. Can any type of wave exhibit interference through double slits?

Yes, any type of wave can exhibit interference through double slits, as long as the wave has a wavelength that is similar to the slit separation. This includes not only visible light, but also other electromagnetic waves such as radio waves and microwaves, as well as sound waves and water waves.

5. How does the intensity of the light affect the interference pattern?

The intensity of the light, or its brightness, does not affect the interference pattern. The interference pattern is solely determined by the wavelength of the light and the slit separation. However, a higher intensity light source will produce a brighter interference pattern, making it easier to observe and measure the fringes.

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