How is the angular width of the central maximum found?

The angular width of the central maximum is found using the formula θ = λ / b, where λ is the wavelength and b is the slit width.

In the study of light and optics, the angular width of the central maximum is a key concept in understanding diffraction and interference patterns. This is particularly relevant when light passes through a single slit, creating a diffraction pattern with a central maximum and several smaller maxima on either side. The angular width of this central maximum can be calculated using the formula θ = λ / b, where λ represents the wavelength of the light and b is the width of the slit.

The formula is derived from the principle of superposition, which states that when two or more waves overlap, the resultant wave is the sum of the individual waves. When light passes through a slit, it diffracts and spreads out, creating a pattern of light and dark bands. The central maximum is the brightest and widest band, and its angular width can be calculated using the aforementioned formula.

To use the formula, you need to know the wavelength of the light and the width of the slit. The wavelength is usually given in nanometres (nm), and the slit width in metres (m). The result, θ, is the angular width of the central maximum, given in radians. To convert this to degrees, you can multiply by 180/π.

It's important to note that this formula gives the angular width between the first minima on either side of the central maximum. This is because the intensity of the light decreases rapidly after the central maximum, reaching a minimum before increasing again to form the next maximum. The points at which the intensity reaches a minimum are used to define the boundaries of the central maximum.

IB Physics Tutor Summary: The formula θ = λ / b helps calculate the angular width of the central maximum, a bright band seen when light passes through a slit. θ is the angular width in radians, λ the light's wavelength, and b the slit's width. To find θ, measure λ in nanometres and b in metres. To convert θ to degrees, multiply by 180/π. This formula determines the width of the brightest part of the diffraction pattern.