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. **Understanding Fresnel Distance**:
The Fresnel distance (or threshold distance) is the distance at which the ray optics approximation is valid. It is given by the formula:
\[ d = \frac{a^2}{\lambda} \]

2. **Substituting the Wavelength**:
Given that the wavelength \( \lambda = 1 \), we can substitute this value into the formula:
\[ d = \frac{a^2}{1} \]

3. **Simplifying the Expression**:
Since dividing by 1 does not change the value, we simplify the expression:
\[ d = a^2 \]

4. **Conclusion**:
Therefore, the Fresnel distance for the given aperture size \( a \) is:
\[ d = a^2 \]

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

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