Physics · Wave Optics · NEET
At the exact centre, the path difference between waves from every point of the slit is zero, so all wavelets arrive in step and add up fully. This gives maximum brightness. The central maximum stretches from the first minimum on one side to the first minimum on the other side, so it is twice as wide as any secondary maximum (which sits between two neighbouring minima).
The minima (dark bands) occur at a sinθ = nλ (n = 1, 2, 3...). The secondary maxima lie roughly halfway between two minima, at a sinθ = (n + 1/2)λ approximately, that is a sinθ ≈ 3λ/2, 5λ/2, 7λ/2 for the first, second, third secondary maxima. So the FIRST secondary maximum is near a sinθ = 3λ/2.
For a secondary maximum only a small part of the slit contributes waves that add up; the rest cancel in pairs. The larger the angle, the smaller the fraction that survives, so brightness drops fast. The first secondary maximum has only about 4.5% of the central peak intensity, the next even less.
No. Double slit gives many equally bright, equally spaced fringes from TWO sources interfering. Single slit gives ONE dominant bright centre with fading side maxima, from waves within ONE slit. In a real double-slit pattern the sharp interference fringes actually sit inside a single-slit diffraction envelope.
Narrower slit (smaller a) spreads the pattern MORE. Since a sinθ = λ for the first minimum, a smaller a means a larger θ, so the central maximum becomes wider. A wide slit gives a narrow bright line close to ray optics.
In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle 30 degrees when light of wavelength 5000 A is incident on the slit. The first secondary maximum is observed at an angle of
A linear aperture of width 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 x 10⁻⁵ cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Every point of the slit acts as a source of secondary wavelets (Huygens' principle). These wavelets travel in all forward directions and overlap on the screen. Where they add in step you get bright bands; where they cancel you get dark bands. This spreading of light on passing a narrow slit is diffraction.
The central maximum is twice as wide as each secondary maximum. It runs between the first minimum on each side, while a secondary maximum sits between two neighbouring minima.
About 4.5% of the central maximum's intensity (roughly 1/22). The second secondary maximum is even fainter, around 1.6%. This is why side bands look weak next to the bright centre.
Approximately a sinθ = (n + 1/2)λ, that is a sinθ ≈ 3λ/2, 5λ/2, 7λ/2 for n = 1, 2, 3. Remember the minima use a sinθ = nλ.
Yes. The width of the central maximum is proportional to wavelength (a sinθ = λ for the first minimum). Red light (longer λ) spreads more than blue light, so the central maximum is wider for red.
