Question

Fresnel distance for an aperture of size $a$ illuminated by a parallel beam of light of wavelength $\lambda$, deciding the validity of ray optics is

• A. $\frac{\lambda }{a^2}$
• B. $\lambda a$
• C. $a^2\lambda$
• D. $\frac{a^2}{\lambda }$
• E. $a^2{\lambda }^2$

Answer 1

Answer: (D)

When a slit or hole size $a$ is illuminated by a parallel beam, then it is diffracted at an angle of $\frac{\lambda }{a}$.
In travelling a distance $z$, size of beam is $\frac{z\lambda }{a}$.
So, $\frac{z\lambda }{a}\ge a$
or $z\ge \frac{a^2}{\lambda }$
where, $z$ is Fresnel's distance. So, image formation can be explained by ray optics for distance less than $z_f$.