Light of wavelength 560 nm goes through a pinhole of diameter 0.20 mm and falls on a wall at a distance of 2.00 m. What will be the radius of the central bright spot formed on the wall ?

Explanation

To find the radius of the central bright spot formed on the wall when light passes through a pinhole, we can use the formula for the radius of the central maximum in a single-slit diffraction pattern:

\[ R = \frac{1.22 \lambda D}{d} \]

where:
- \( R \) is the radius of the central bright spot,
- \( \lambda \) is the wavelength of the light,
- \( D \) is the distance from the pinhole to the wall,
- \( d \) is the diameter of the pinhole.

### Step-by-Step Solution:

1. **Identify the given values**:
- Wavelength of light, \( \lambda = 560 \, \text{nm} = 560 \times 10^{-9} \, \text{m} \)
- Diameter of the pinhole, \( d = 0.20 \, \text{mm} = 0.20 \times 10^{-3} \, \text{m} \)
- Distance from the pinhole to the wall, \( D = 2.00 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ R = \frac{1.22 \times (560 \times 10^{-9}) \times 2}{0.20 \times 10^{-3}} \]

3. **Calculate the numerator**:
- First, calculate \( 1.22 \times 560 \times 10^{-9} \):
\[ 1.22 \times 560 = 683.2 \times 10^{-9} \]
- Then multiply by \( 2 \):
\[ 683.2 \times 10^{-9} \times 2 = 1366.4 \times 10^{-9} \, \text{m} \]

4. **Calculate the denominator**:
- Convert the diameter to meters:
\[ d = 0.20 \times 10^{-3} \, \text{m} = 0.0002 \, \text{m} \]

5. **Now, divide the numerator by the denominator**:
\[ R = \frac{1366.4 \times 10^{-9}}{0.0002} = 6.832 \times 10^{-3} \, \text{m} \]

6. **Convert the radius to centimeters**:
\[ R = 6.832 \times 10^{-3} \, \text{m} = 0.6832 \, \text{cm} \]

7. **Final answer**:
The radius of the central bright spot formed on the wall is approximately \( 0.683 \, \text{cm} \).