In Young's double-slit experiment, the interference pattern observed on a screen occurs when light passes through two closely spaced slits, creating two coherent sources of light waves. The intensity of the fringes, or the brightness of the interference pattern, is affected by the distance between the screen and the slits.
When the distance between the screen and the slits is increased, the intensity of the fringes decreases. This decrease in intensity can be understood through the phenomenon of diffraction.
Diffraction is the bending or spreading out of waves as they encounter an obstacle or a narrow slit. In the case of the double-slit experiment, as the distance between the screen and the slits is increased, the waves from each slit spread out more before reaching the screen. This spreading out of the waves results in a wider interference pattern on the screen.
The wider interference pattern means that the intensity of each individual fringe decreases because the same amount of light is spread over a larger area. This leads to a decrease in the overall brightness of the fringes.
Mathematically, the intensity of the fringes in the double-slit experiment can be described by the equation:
I = 4I₀cos²(πd sinθ / λ)
where I is the intensity at a particular point on the screen, I₀ is the maximum intensity at the center of the pattern, d is the distance between the slits, θ is the angle at which the light waves diffract, and λ is the wavelength of light.
As the distance between the screen and the slits increases (larger d), the term πd sinθ / λ increases, causing the cosine term to decrease, and thus reducing the intensity of the fringes.
In summary, increasing the distance between the screen and the slits in Young's double-slit experiment leads to a decrease in the intensity of the fringes due to the phenomenon of diffraction, which causes the interference pattern to spread out over a larger area on the screen.