Animated Solution for Physics - Optics: Yellow light is used in a single slit diffraction experiment with slit width of $0.6\text{ mm}$. If yellow light is replaced by X-rays, then the observed pattern will reveal

Have you ever wondered why you can hear someone talking around a corner, but you can't see them? It all comes down to diffraction—the bending of waves around obstacles. But diffraction doesn't just happen willy-nilly. There is a strict, non-negotiable rule: the wavelength of the wave must be comparable to the size of the obstacle or slit.

Mathematically, we write this as $\lambda \sim a$, where $\lambda$ is the wavelength and $a$ is the slit width. If the wavelength is too small, the wave just marches straight ahead, ignoring the edges completely.

In our experiment, we start with yellow light passing through a slit of width $a=0.6\text{ mm}$.

Now, the wavelength of yellow light is roughly ${\lambda }_{\text{yellow}}\approx 600\text{ nm}$, which is $6\times 10^{-4}\text{ mm}$. While this is smaller than the slit width, it is still large enough to interact with the edges of the slit.

Because of this interaction, the light waves bend and interfere with each other, creating a beautiful, spread-out diffraction pattern on the screen, complete with a central maximum and alternating bright and dark fringes.

But what happens when we swap the yellow light for X-rays? This is where things get interesting.

X-rays are highly energetic electromagnetic waves with incredibly tiny wavelengths, typically around ${\lambda }_{\text{X-ray}}\approx 1\text{ A˚}$ (which is $10^{-10}\text{ m}$).

Let's compare this to our slit width:

The wavelength of the X-rays is millions of times smaller than the slit! Because $\lambda \ll a$, the X-rays don't "feel" the edges of the slit. They exhibit rectilinear propagation, meaning they travel in perfectly straight lines.

Since the X-rays don't bend, no diffraction pattern is formed. Instead, the X-rays pass straight through the $0.6\text{ mm}$ opening and cast a sharp, well-defined rectangular shadow on the screen, exactly the same size as the slit itself.

If we ever wanted to diffract X-rays, we would need a "slit" that is much, much smaller—something on the order of $1\text{ A˚}$. This is exactly why scientists use the natural spacing between atoms in crystal lattices to diffract X-rays!