A slit 5 cm wide when irradiated by waves of wavelength 10 mm results in the angular spread of the central maxima on either side of incident light by about :

Options

A. `1/5` radian
B. 4 radian
C. 5 radian
D. 6 radian

Answer

To solve the problem of finding the angular spread of the central maxima when a slit of width 5 cm is irradiated by waves of wavelength 10 mm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Width of the slit (d) = 5 cm
- Wavelength of the waves (λ) = 10 mm

2. **Convert Units:**
- Convert the width of the slit from centimeters to millimeters for consistency.
\[ d = 5 \text{ cm} = 50 \text{ mm} \]

3. **Use the Formula for Angular Spread:**
- The formula for the angular spread (θ) of the central maxima in a single-slit diffraction pattern is given by:
\[ \theta = \frac{\lambda}{d} \]

4. **Substitute the Values into the Formula:**
- Substitute λ = 10 mm and d = 50 mm into the formula:
\[ \theta = \frac{10 \text{ mm}}{50 \text{ mm}} = \frac{1}{5} \text{ radians} \]

5. **Conclusion:**
- The angular spread of the central maxima on either side of the incident light is:
\[ \theta = \frac{1}{5} \text{ radians} \]

### Final Answer:
The angular spread of the central maxima is \( \frac{1}{5} \) radians.