In a Young's double slit experiment, (slit distance d) monochromatic light of wavelength `lambda` is used and the fringe pattern observed at a distance D from the slits. The angular position of the bright fringes are

Options

A. ` "sin"^(-1)((N lambda)/(d))`
B. ` "sin"^(-1)(((N+(1)/(2)) lambda)/(d))`
C. ` "sin"^(-1)((N lambda)/(D))`
D. ` "sin"^(-1)(((N+(1)/(2)) lambda)/(D))`

Explanation

To find the angular position of the bright fringes in a Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
In a Young's double slit experiment, we have two slits separated by a distance \(d\) and a screen placed at a distance \(D\) from the slits. Monochromatic light of wavelength \(\lambda\) is used.

2. **Identify the Path Difference**:
The path difference \(\Delta x\) between the light waves coming from the two slits to a point on the screen is given by:
\[ \Delta x = \frac{d \cdot y}{D} \]
where \(y\) is the distance from the central maximum to the point of interest on the screen.

3. **Condition for Bright Fringes**:
For constructive interference (bright fringes), the path difference must be an integer multiple of the wavelength:
\[ \Delta x = n\lambda \]
where \(n\) is an integer (0, 1, 2, ...).

4. **Set Up the Equation**:
Equating the two expressions for path difference:
\[ \frac{d \cdot y}{D} = n\lambda \]

5. **Rearrange to Find \(y\)**:
Rearranging gives:
\[ y = \frac{n\lambda D}{d} \]

6. **Find the Angular Position**:
The angular position \(\theta\) of the bright fringe can be found using the small angle approximation:
\[ \sin \theta \approx \tan \theta = \frac{y}{D} \]
Substituting for \(y\):
\[ \sin \theta \approx \frac{n\lambda D}{dD} = \frac{n\lambda}{d} \]

7. **Final Expression for Angular Position**:
Thus, the angular position of the bright fringes is given by:
\[ \theta = \sin^{-1}\left(\frac{n\lambda}{d}\right) \]

### Summary:
The angular position of the bright fringes in a Young's double slit experiment is:
\[ \theta = \sin^{-1}\left(\frac{n\lambda}{d}\right) \]