Question

In Young’s double slit experiment, if the distance between the slits is increased while keeping all other parameters constant, the fringe width will:

• A. Increase
• B. Decrease
• C. Remain unchanged
• D. First increase then decrease

Hint:

Remember the inverse relationship: $\beta \propto \frac{1}{d}$. If you push the two slits further apart ($d \uparrow$), the interference pattern on the screen shrinks and compresses, meaning the fringe width must decrease ($\beta \downarrow$).

Answer 1

The Correct Option is B

Concept: In Young's Double Slit Experiment (YDSE), the spatial separation between consecutive bright or dark fringes on the screen is defined as the fringe width ($\beta$). The mathematical formula governing the fringe width is given by: \[ \beta = \frac{\lambda D}{d} \] Where:
• $\lambda$ is the wavelength of the monochromatic light source used.
• $D$ is the perpendicular distance between the plane containing the double slits and the observation screen.
• $d$ is the distance between the two slits ($S_1$ and $S_2$).

Step 1: Analyze the mathematical relationship between variables.
From the standard formula, we can isolate how the fringe width $\beta$ reacts specifically to adjustments in the slit separation distance $d$ when the wavelength $\lambda$ and the screen distance $D$ are held completely constant: \[ \beta \propto \frac{1}{d} \] This demonstrates an inverse proportionality between the fringe width and the distance separating the two slits.

Step 2: Evaluate the effect of increasing the slit distance.
Because $\beta$ and $d$ are inversely proportional, any increase in the slit separation distance $d$ will automatically cause the fringe width $\beta$ to diminish. Physically, this means the interference fringes on the observation screen will contract and pack closer together.