Question

Effect of diffraction can be neglected when the distance between screen and lens/slit is less than or equal to $\frac{{\mathrm{a}}^2}{\mathrm{\lambda }}$

• A. greater than $\frac{a^2}{\lambda }$
• B. less than $\frac{a^2}{\lambda }$
• C. any value greater than $50\lambda$
• D. more than $10\mathrm{km}$

Answer 1

The correct option is B

less than $\frac{a^2}{\lambda }$

Explanation of correct option:

1. Ray optics is based on the assumption that light travels in a straight line but wave optics (especially the diffraction effect) is based on the assumption that light doesn’t travel in a straight light, it bends around the edge.

2. We know that the linear width $\left(x\right)$ of central maxima from the center is

$x=\frac{D\lambda }{a}$

Here, $a$ is the size of the aperture, $D$ is the distance between the slit and the screen, and $\lambda$ is the wavelength of the light used.

3. It is clear from the relation, if $x$ is small, then ray optics is valid.

4. The distance $\left(D\right)$ at which the diffraction spread $\left(x\right)$ of a beam of light is equal to the size of the aperture $\left(a\right)$ is called Fresnel Distance. It is denoted by $Z_f$

Now,

$$\begin{gathered} x=\frac{D\lambda }{a} \\ \Rightarrow a=\frac{Z_f\lambda }{a} \end{gathered}$$

Therefore, Fresnel distance is given as $Z_f=\frac{a^2}{\lambda }$

5. If $D<Z_f$, then diffraction effects can be neglected and ray optics is valid.

6. If $D\gg Z_f$, the spreading due to diffraction is very pronounced and ray optics is not valid.

Thus, the effect of diffraction can be neglected when the distance between screen and slit is less than or equal to $\frac{{\mathrm{a}}^2}{\mathrm{\lambda }}$.

Therefore, option (B) is correct.