Animated Solution for Physics - Optics: If the source of light used in a Young's double slit experiment is changed from red to violet, then

Imagine you are in a dark room performing Young's Double Slit Experiment. You have a light source, two tiny slits, and a screen where a beautiful interference pattern of bright and dark fringes is formed. This classic experiment is the ultimate proof of the wave nature of light, but it also hides some beautiful mathematical symmetries.

Let's look at the math behind this pattern. The distance between two consecutive bright fringes, which we call the fringe width $\beta$, depends on three fundamental parameters: the wavelength of the light $\lambda$, the distance to the screen $D$, and the slit separation $d$.

This relationship is elegantly captured by the formula:

Notice that the fringe width $\beta$ is directly proportional to the wavelength $\lambda$. This means that if we change the color of the light, we are directly manipulating the spacing of our interference pattern.

If we use a red light source, the wavelength ${\lambda }_{red}$ is relatively large (around $700\text{ nm}$). Because of the direct proportionality, the red fringes will be wider and spread out across the screen.

But what happens if we swap the red light for a violet one? We know from the visible spectrum that violet light has a much shorter wavelength than red light (around $400\text{ nm}$).

Since the fringe width is directly proportional to the wavelength, a smaller wavelength mathematically guarantees a smaller fringe width.

Physically, this means the fringes will shrink and pack closely together. Therefore, the consecutive fringe lines will come closer to each other. The entire pattern becomes more compressed. It is a simple yet elegant consequence of the wave nature of light.