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May 15

# What is formular calculation for interference single slit and double slits?

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May 15
The formula for calculating the interference pattern produced by a single slit is given by:

$I(\theta) = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2$

where:
- $$I(\theta)$$ is the intensity of the interference pattern at an angle $$\theta$$ from the central maximum
- $$I_0$$ is the intensity of the central maximum
- $$\beta = \frac{\pi a \sin(\theta)}{\lambda}$$ is the phase difference between waves passing through the slit
- $$a$$ is the width of the slit
- $$\lambda$$ is the wavelength of the light

The formula for calculating the interference pattern produced by double slits is given by:

$I(\theta) = I_0 \cos^2 \left( \frac{\pi d \sin(\theta)}{\lambda} \right)$

where:
- $$I(\theta)$$ is the intensity of the interference pattern at an angle $$\theta$$ from the central maximum
- $$I_0$$ is the intensity of the central maximum
- $$d$$ is the distance between the two slits
- $$\lambda$$ is the wavelength of the light

These formulas can be used to calculate the intensity of the interference pattern at different angles for both single and double slit setups.
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May 15
Single Slit Interference

- Intensity:


I = I₀ (sin(πa sin θ)/πa sin θ)²


where:
- I₀ is the maximum intensity
- a is the slit width
- θ is the angle between the central maximum and the point on the wavefront
- π is a constant

- Distance between bright fringes:


d = λD/a


where:
- λ is the wavelength of light
- D is the distance between the slit and the screen
- a is the slit width

Double Slit Interference

- Intensity:


I = I₀ (cos(πd sin θ)/cos(πa sin θ))²


where:
- I₀ is the maximum intensity
- d is the distance between the slits
- a is the width of each slit
- θ is the angle between the central maximum and the point on the wavefront
- π is a constant

- Distance between bright fringes:


d = λD/(d + a)


where:
- λ is the wavelength of light
- D is the distance between the slits and the screen
- d is the distance between the slits
- a is the width of each slit
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