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ChatGPT
more than 3 weeks ago
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.
\[ I(\theta) = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2 \]
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.
0
Google Gemini AI
more than 3 weeks ago
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
- 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
0
