The Young's double-slit experiment is a classic experiment that demonstrates the interference of light and provides evidence for the wave nature of light. Here's a description of the experiment and a derivation of the expression for fringe spacing:
Experimental Setup:
- Take a thin sheet of material, such as cardboard, and make two narrow, closely spaced slits in it. These slits should be parallel to each other and small enough to act as point sources of light.
- Illuminate the slits with a coherent light source, such as a laser or a monochromatic light bulb. Coherence ensures that the light waves emitted from the two slits maintain a fixed phase relationship.
- Place a screen a distance away from the slits to observe the interference pattern.
Interference Pattern: When light passes through the double slits, each slit acts as a source of secondary waves. These secondary waves propagate outward and overlap on the screen. The overlapping waves interfere with each other, resulting in an interference pattern on the screen.
Derivation of Fringe Spacing: Let's consider a point on the screen that is a distance "y" from the central maximum (the point on the screen directly in line with the center of the slits). The path difference between the waves from the two slits reaching this point is given by: Δx = d sinθ
In the above equation:
- Δx is the path difference between the waves from the two slits.
- d is the distance between the slits.
- θ is the angle between the line drawn from the center of the slits to the point on the screen and the line drawn perpendicular to the slits.
Due to interference, constructive interference occurs when the path difference is an integer multiple of the wavelength (λ) of light: Δx = mλ
From the geometry of the setup, we have: sinθ = y / D
In the above equation:
- y is the distance of the point on the screen from the central maximum.
- D is the distance between the slits and the screen.
Combining the above equations, we get: d sinθ = mλ
Solving for y, we have: y = (mλD) / d
The above equation represents the position of the bright fringes (constructive interference) on the screen. The fringe spacing (distance between adjacent bright fringes) is given by the difference in the positions of adjacent bright fringes: Δy = [(m + 1)λD / d] - [mλD / d] = (λD) / d
The expression for fringe spacing (Δy) shows that it depends on the wavelength of light (λ), the distance between the slits and the screen (D), and the distance between the slits (d). It demonstrates that as the slit spacing decreases or the wavelength increases, the fringes become closer together, resulting in a more tightly packed interference pattern.