The angular size of the central maxima due to a single slit diffraction is (a `to` slit width)

Options

A. `lamda/a`
B. `(2lamda)/(a)`
C. `(3lamda)/(2a)`
D. `(lamda)/(2a)`

Answer

To find the angular size of the central maxima due to single slit diffraction, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Single Slit Diffraction**:
In single slit diffraction, light passing through a narrow slit creates a pattern of bright and dark fringes on a screen. The central maximum is the brightest part of the pattern, and it is flanked by dark minima.

2. **Identifying the First Minimum**:
The position of the first minimum in the diffraction pattern is given by the condition:
\[ A \sin \theta = \lambda \]
where:
- \( A \) is the width of the slit,
- \( \lambda \) is the wavelength of the light,
- \( \theta \) is the angle at which the first minimum occurs.

3. **Finding \(\sin \theta\)**:
Rearranging the equation gives:
\[ \sin \theta = \frac{\lambda}{A} \]

4. **Small Angle Approximation**:
For small angles, we can use the approximation \(\sin \theta \approx \theta\) (in radians). Thus, we have:
\[ \theta \approx \frac{\lambda}{A} \]

5. **Calculating the Angular Size of the Central Maxima**:
The angular size of the central maximum is defined as the angle from the first minimum on one side to the first minimum on the other side. Therefore, the total angular size is:
\[ \text{Angular Size} = 2\theta \approx 2 \left(\frac{\lambda}{A}\right) \]

6. **Final Expression**:
Thus, the angular size of the central maxima due to single slit diffraction is:
\[ \text{Angular Size} = \frac{2\lambda}{A} \]