Question

Explain the term fresnel distance.

Answer 1

Step 1: Fresnel Distance,

1. Fresnel distance is the distance between the screen and the slit at which the dispersion of light due to diffraction from the center of the screen is exactly equal to the size of the slit or Fresnel distance is defined as the minimum distance that is traveled by a ray of light along the linear path before diffraction.
2. This is where ray optics and wave optics meet.
3. Fresnel Distance is denoted as $Z_f$

Step 2: Derivation of Fresnel distance,

Consider a single slit of thickness $\text{'}a\text{'}$ in an aperture. There will be a diffraction pattern visible.

The angular size of the central maximum = $\frac{\lambda }{a}$

$\text{'}z\text{'}$ is the distance traveled by light waves before the spread occurs,

The spread is given as = $z\frac{\lambda }{a}$ ……… equation (1)

$a=z\frac{\lambda }{a}$ ……….equation (2) where $a$ =width of the diffracted beam.

From equation(1) and equation (2), we get,

$z\approx \frac{a^2}{\lambda }$

This distance is known as Fresnel distance.