Understanding Single Slit Diffraction

Single slit diffraction is a phenomenon observed when light passes through a narrow opening (slit). Instead of projecting a sharp shadow of the slit, a pattern of bright and dark bands, called fringes, appears on a screen placed behind the slit. The brightest fringe is located at the center and is known as the central maximum.

Analyzing Central Maximum Width vs. Slit Width

In the single-slit diffraction pattern, the bright fringes are separated by dark fringes called minima. The position of these minima is determined by the slit width ($a$), the wavelength of light ($\lambda$), and the angle of diffraction ($\theta$).

The condition for the first minimum (the dark band on either side of the central maximum) is given by the formula:

$$a \sin(\theta) = \lambda$$

Where:

• $a$ = width of the slit
• $\theta$ = angle of diffraction for the first minimum
• $\lambda$ = wavelength of the light

For small angles, which is common in diffraction experiments, we can approximate $\sin(\theta) \approx \theta$ (where $\theta$ is in radians). Thus, the equation becomes:

$$a \theta \approx \lambda$$

This gives us the angle for the first minimum:

$$\theta \approx \frac{\lambda}{a}$$

The central maximum extends from the first minimum on one side ($-\theta$) to the first minimum on the other side ($+\theta$). Therefore, the total angular width ($\Delta \theta$) of the central maximum is:

$$\Delta \theta = \theta - (-\theta) = 2\theta$$

Substituting the expression for $\theta$:

$$\Delta \theta \approx \frac{2\lambda}{a}$$

From this equation, we can see that the angular width of the central maximum ($\Delta \theta$) is inversely proportional to the slit width ($a$).

Conclusion on Changing Slit Width

Based on the relationship $\Delta \theta \propto \frac{1}{a}$:

• If the slit width ($a$) increases, the denominator in the fraction $\frac{2\lambda}{a}$ gets larger.
• This causes the value of $\Delta \theta$ to become smaller.

Therefore, as the slit width increases, the angular width of the central maximum decreases. The central bright spot becomes narrower.

The correct option is that it will decrease.