Q.Answer the following questions:

This is a five-part conceptual set covering slit-width effects, the diffraction envelope of a double-slit pattern, the diffraction origin of the Poisson bright spot, why light (unlike sound) can't bend around a room partition, and why ray optics still works for ordinary …

1. Doubling the slit width In single-slit diffraction, the angular half-width of the central maximum is $\theta \approx \lambda/a$. Doubling the slit width $a \to 2a$ halves this angular width, so the central diffraction band becomes narrower (half its original angular size). At the same time, since twice as much light passes through the wider slit, the amplitude at the centre (which adds up constructively from every point across the slit) doubles, and since intensity $\propto (\text{amplitude})^2$, the intensity at the centre becomes four times as large.
2. Diffraction and the double-slit interference pattern The observed double-slit pattern is not pure interference fringes of uniform brightness — it is the fine, closely-spaced interference fringes (set by the slit separation $d$) modulated by the broader single-slit diffraction envelope (set by each slit's own width $a$). The diffraction pattern of a single slit acts as an envelope that limits how bright each interference fringe can be — fringes near a diffraction minimum are strongly suppressed, and no interference fringes are visible outside the central diffraction envelope.
3. The bright spot at the centre of a circular obstacle's shadow Every point on the rim (edge) of a small circular obstacle is, by symmetry, exactly the same distance from the centre point of the shadow directly behind it. Light diffracted from all points around the rim therefore travels equal path lengths to reach that centre point, arriving there exactly in phase, and interferes constructively — producing a bright spot at the very centre of the geometrical shadow. (This is the famous Poisson's spot, first predicted as a seemingly absurd consequence of Fresnel's wave theory and then experimentally confirmed by Arago — becoming one of the strongest pieces of evidence for the wave nature of light.)
4. Why the partition blocks light but not sound Appreciable diffraction (bending around an obstacle) occurs only when the size of the obstacle is comparable to the wavelength of the wave. Audible sound has wavelengths of the order of centimetres to metres — comparable to the $7\ \text{m}$ partition wall — so sound diffracts around it easily and reaches the other side. Visible light has a wavelength of only about $5\times10^{-7}\ \text{m}$, many orders of magnitude smaller than the $7\ \text{m}$ wall, so light diffracts negligibly around it and travels essentially in straight lines — the students can hear each other but cannot see each other. …