For an aperture of size a illuminated by a parallel beam of light having wavelength 1, the Fresnel distance is:

Options

A. `=a//lambda`
B. `=a^(2)//lambda`
C. `=a^(2)lambda`
D. `=a//lambda^(2)`

Answer

To find the Fresnel distance for an aperture of size \( a \) illuminated by a parallel beam of light with a wavelength \( \lambda = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Fresnel Distance**:
The Fresnel distance (\( D_f \)) is a measure of the distance over which wave effects become significant in the propagation of light. It is given by the formula:
\[ D_f = \frac{a^2}{\lambda} \]
where \( a \) is the size of the aperture and \( \lambda \) is the wavelength of the light.

2. **Substitute the Given Values**:
In this problem, we know that the size of the aperture is \( a \) and the wavelength \( \lambda \) is given as 1. Therefore, we can substitute these values into the formula:
\[ D_f = \frac{a^2}{1} \]

3. **Simplify the Expression**:
Since \( \lambda = 1 \), the expression simplifies to:
\[ D_f = a^2 \]

4. **Conclusion**:
The Fresnel distance for the given aperture size \( a \) and wavelength \( \lambda = 1 \) is:
\[ D_f = a^2 \]

### Final Answer:
The Fresnel distance is \( a^2 \).

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