**CBSE NOTES CLASS 12 PHYSICS **

**CHAPTER 10 WAVE OPTICS**

**Fresnel distance**

The angle of diffraction due to an aperture (i.e., slit or hole) of size *a* illuminated by a parallel beam is $\frac{\lambda}{a}$. This is the angular size of the bright central maximum. In travelling a distance *z*, the diffracted beam acquires a width $\frac{z\lambda}{a}$ due to diffraction.

The distance beyond which the divergence of beam of width ‘*a*’ becomes significant is called Fresnel distance, at which point, is denoted by z_{F}

$$\frac{{\mathrm{z}}_{\mathrm{F}}\mathrm{\lambda}}{\mathrm{a}}=\mathrm{a}\mathrm{}\mathrm{}\mathrm{}\mathrm{}$$

$$\Rightarrow \mathrm{}{\mathrm{z}}_{\mathrm{F}}\mathrm{\lambda}=\mathrm{}{\mathrm{a}}^{2}\mathrm{}\mathrm{}$$

$$\Rightarrow \mathrm{}{\mathrm{z}}_{\mathrm{F}}=\mathrm{}\frac{{\mathrm{a}}^{2}}{\mathrm{\lambda}}\mathrm{}$$

For distances much smaller than z_{F}, the spreading due to diffraction is smaller compared to the size of the beam. It becomes comparable when the distance is approximately z_{F}. For distances much greater than z_{F}, the spreading due to diffraction dominates over that due to ray optics (i.e., the size ‘*a*’ of the aperture). The ray optics is valid in the limit of wavelength tending to zero.