‘Suppose that the central diffraction maximum for two slits contains 17 interference fringes for some wavelength of light: How many interference fringes would you expect in the first secondary diffraction maximum?’
The Correct Answer and Explanation is:
Correct Answer: 16 interference fringes
Explanation:
To solve this, we need to understand the interaction between diffraction and interference in a double-slit experiment.
In a typical double-slit setup, the light passes through two slits and spreads out, creating two overlapping patterns:
- Diffraction pattern due to each slit acting like a single aperture
- Interference pattern due to the interaction between light waves from the two slits
The central diffraction maximum is the broad central band formed due to the diffraction of light through the slits. Within this broad envelope, several interference fringes are observed as a result of constructive and destructive interference.
We are told that 17 interference fringes fit within the central diffraction maximum. This number includes the central bright fringe and 8 fringes on each side (symmetrically located). These interference fringes occur within the first diffraction minimum on either side of the central maximum.
Now, we are asked to determine how many interference fringes fall within the first secondary diffraction maximum, which is the region between the first and second diffraction minima.
The number of interference fringes between two successive diffraction minima is generally one less than the number in the central diffraction maximum. This is because the width of the diffraction envelope determines how many bright interference bands are allowed in each region.
Since 17 fringes are observed within the central diffraction maximum, each side of the central maximum has 8 fringes. In the next diffraction region (the first secondary maximum), the intensity is lower and narrower, and it allows only 16 fringes (8 on each side minus the central one, which only exists in the central maximum).
Therefore, we expect 16 interference fringes in the first secondary diffraction maximum — 8 on each side of the new central point within that region.
