How does the width of the central region of a single-slit diffraction pattern change as the wavelength of the light increases?
Look at the formula on this.
d*sin(theta)=m(lamda)
d=m(lamda)/sin(theta)
so as lamda increases the central region increases its proportional
To understand how the width of the central region of a single-slit diffraction pattern changes with the wavelength of light, we need to look at the equation that determines the angular position of the first minimum in the pattern. The equation is known as the single-slit diffraction formula:
sin(θ) = mλ/d
In this equation:
- θ represents the angle between the central bright fringe and the first minimum.
- m is the order of the minimum (m = 1 for the first minimum).
- λ is the wavelength of the light.
- d is the width of the slit.
To determine how the width of the central region changes with the wavelength, we can focus on θ, the angular position of the first minimum. As we can see from the formula, when the wavelength increases, the value of θ decreases.
Now, the central region of the diffraction pattern corresponds to the region where θ is small, which means that the angle between the central bright fringe and the first minimum is small. Therefore, as the wavelength increases, the width of the central region increases.
In simpler terms, if we consider a fixed distance between the central bright fringe and the first minimum, as the light's wavelength increases, the width of the central region becomes broader.
Keep in mind that this explanation assumes that the width of the slit (d) remains constant. If the width of the slit changes, it will affect the diffraction pattern as well.