In the Young's double-slit experiment (YDSE), the interference pattern we observe is a result of the superposition of light waves coming from two slits. When you have two slits with different intensities, the resulting interference pattern is influenced by the amplitudes of the light waves from each slit. Let's break down what happens when you adjust the intensity of the second slit to match that of the first slit.
Understanding Intensity and Amplitude
The intensity of light is proportional to the square of the amplitude of the wave. So, if the first slit has an intensity of I, its amplitude can be represented as A. For the second slit, if its initial intensity is I/4, its amplitude would be A/2. When you increase the intensity of the second slit to match the first, its amplitude becomes equal to A as well.
Interference Pattern Basics
The interference pattern is created by the constructive and destructive interference of the light waves from the two slits. Constructive interference occurs when the waves are in phase, leading to bright fringes, while destructive interference occurs when they are out of phase, resulting in dark fringes.
Effect of Equal Intensities
When both slits have the same intensity, the amplitudes of the waves are equal. This means that the maximum intensity of the bright fringes will increase, but the overall pattern of bright and dark fringes remains unchanged. The reason for this is that the positions of the fringes depend on the path difference between the two waves, not their individual intensities.
- Bright Fringes: The intensity at the bright fringes is given by the formula I_max = (A1 + A2)², where A1 and A2 are the amplitudes from the two slits. When both amplitudes are equal, the maximum intensity increases, but the fringe positions remain the same.
- Dark Fringes: The intensity at the dark fringes is determined by the condition where the waves cancel each other out (A1 - A2 = 0). Since both amplitudes are now equal, the dark fringes will still occur at the same positions as before.
Why the Observed Intensity Doesn't Change
Even though the individual intensities of the slits are equal, the interference pattern's characteristics—specifically the spacing and position of the fringes—are determined by the wavelength of the light and the distance between the slits. Thus, while the maximum intensity of the bright fringes may increase, the overall pattern remains unchanged. The observed intensity of the bright and dark fringes does not increase in terms of their relative positions and spacing; it simply becomes more pronounced.
In summary, increasing the intensity of the second slit to match the first does enhance the brightness of the bright fringes, but it does not alter the fundamental interference pattern. The positions of the bright and dark fringes remain constant, which is why the observed intensity of the dark and bright fringes does not change in terms of their relative visibility in the pattern.
