The angular width of the central maximum in a diffraction pattern can be calculated using the formula

where $\lambda$ represents the wavelength of the light and $b$ is the width of the slit.

In the realm of light and optics, understanding the angular width of the central maximum is crucial for comprehending diffraction phenomena. This concept becomes particularly significant when light passes through a single slit, resulting in a diffraction pattern characterized by a prominent central maximum accompanied by smaller maxima on either side. The angular width of the central maximum can be determined using the aforementioned formula.

This formula is derived from the principle of superposition, which asserts that when two or more waves overlap, the resultant wave is the sum of the individual waves. As light travels through a slit, it undergoes diffraction, spreading out and forming a pattern of alternating light and dark bands. The central maximum is the most intense and widest band, and its angular width can be computed with the formula provided.

To apply the formula, one must know both the wavelength of the light and the width of the slit. The wavelength is typically measured in nanometers (nm), while the slit width is measured in meters (m). The resulting value of $\theta$ represents the angular width of the central maximum in radians. To convert this value to degrees, one can multiply by $\frac{180}{\pi}$.

It is important to emphasize that this formula calculates the angular width between the first minima on either side of the central maximum. This is because the intensity of light diminishes rapidly after the central maximum, reaching a minimum before increasing again to form the subsequent maximum. The locations where the intensity reaches a minimum are utilized to define the boundaries of the central maximum.

In summary, the formula

is essential for calculating the angular width of the central maximum, which is the brightest band observed when light passes through a slit. In this equation, $\theta$ denotes the angular width in radians, $\lambda$ is the wavelength of the light, and $b$ is the width of the slit. To find $\theta$, measure $\lambda$ in nanometers and $b$ in meters. To convert $\theta$ to degrees, simply multiply by $\frac{180}{\pi}$. This formula effectively quantifies the width of the brightest region in the diffraction pattern.