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Anonymous
more than 4 weeks ago

Is there any standard use to calculate the unknown of theata when wavelength on distance ?

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ChatGPT
more than 4 weeks ago
Yes, there is a standard formula to calculate the unknown angle theta when given the wavelength and distance. This formula is known as the diffraction formula and is given by:

sin(theta) = m * lambda / d

Where:
- theta is the unknown angle
- lambda is the wavelength of the light
- d is the distance between the source of light and the screen
- m is the order of the diffraction maximum

By rearranging this formula, you can solve for the unknown angle theta.
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G
Google Gemini AI
more than 4 weeks ago
Yes, there is a standard method to calculate the unknown angle (theta) when the wavelength and distance are known. This method uses the relationship between the wavelength, distance, and angle in a wave phenomenon, such as diffraction or interference.

The formula for calculating the unknown angle theta is:

```
theta = sin^-1(m - lambda / d)
```

Where:

- theta is the unknown angle (in radians)
- m is the order of the interference or diffraction pattern (for the first order, m = 1)
- lambda is the wavelength of the wave (in meters)
- d is the distance between the slits or obstacles causing the interference or diffraction pattern (in meters)

You can use this formula to calculate the unknown angle theta in various wave phenomena, including:

- Single-slit diffraction
- Double-slit interference
- Diffraction grating
- Interference from thin films
- X-ray crystallography

To use the formula, you need to know the wavelength of the wave and the distance between the slits or obstacles causing the interference or diffraction pattern. You can then measure the angle theta using a protractor or other suitable instrument.

Example:

In a single-slit diffraction experiment, a laser with a wavelength of 632.8 nm (red light) is shone through a slit of width 0.2 mm. A diffraction pattern is observed on a screen 1 meter away from the slit. What is the angle (theta) of the first-order bright fringe on the screen?

Using the formula:

```
theta = sin^-1(m - lambda / d)
```

```
theta = sin^-1(1 - 632.8 nm / 0.2 mm)
```

```
theta = 0.0032 radians
```

Converting radians to degrees:

```
theta = 0.0032 radians - (180 degrees / pi radians)
```

```
theta = 0.184 degrees
```

Therefore, the angle of the first-order bright fringe on the screen is 0.184 degrees.
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