Physical optics in NET covers interference in Young's double slit, diffraction from a single slit, a grating and a crystal, and polarization. Most questions are either a fringe-width ratio or a grating order, and both take one formula each. The one real trap is the highest visible grating order, which worked MCQ 3 below walks through.
Key facts
- Physics is 30% of NET-Engineering, a derived 60 of the 200 MCQs.
- Optics appears twice: first-year Physical Optics and Gravitational Waves (about 6 questions by our estimate) and second-year Physical Optics (about 4).
- Syllabus: two-source interference, single-slit and grating diffraction, resolving power, polarization, and the gravitational waves LIGO detects.
Source: NUST NET-Engineering composition and the SailToNUST physics syllabus, checked October 2026
What the chapter covers
The first-year chapter introduces wavefronts, Huygens' principle, interference, diffraction and polarization, and ends with gravitational waves. The second-year chapter goes back over two-source interference, single-slit and grating diffraction, resolving power and polarization at more depth. For NET, treat them as one chapter. The gravitational-waves section mostly produces concept questions, for example that LIGO detects them with a laser interferometer.
Formulas you need
Coherent sources: same frequency and a constant phase difference
Path difference
constructive (bright) Δ = mλ m = 0, 1, 2 ...
destructive (dark) Δ = (m + ½)λ
Young's double slit (slit gap d, screen distance L)
bright fringe position yₘ = mλL / d
fringe width Δy = λL / d m
Single slit (width a), minima a sinθ = mλ m = 1, 2, 3 ...
Diffraction grating d sinθ = mλ m = 0, ±1, ±2 ...
grating element d = 1 / N (N = lines per metre)
highest order seen m less than d/λ (round down)
Bragg's law (X-rays on a crystal) 2d sinθ = nλ (θ = glancing angle)
Polarization
unpolarized light through one polarizer I = I₀ / 2
Malus's law I = I₀ cos²θ
Brewster angle tan θ_B = n
1 nm = 10⁻⁹ m, 1 Å = 10⁻¹⁰ m
Worked MCQs
1. Changing L and d. In Young's experiment, the slit-to-screen distance is doubled and the slit separation is halved. What happens to the fringe width?
(a) doubles (b) becomes four times (c) halves (d) stays the same
Δy = λL / d
L → 2L, d → d/2 so Δy → (2/(1/2)) Δy = 4Δy
Answer (b).
2. Fringe width with numbers. Light of wavelength 600 nm falls on slits 0.3 mm apart. The screen is 1.5 m away. What is the fringe width?
(a) 0.3 mm (b) 3 mm (c) 30 mm (d) 0.03 mm
Δy = λL / d = (600 × 10⁻⁹ × 1.5) / (0.3 × 10⁻³)
= 9 × 10⁻⁷ / 3 × 10⁻⁴ = 3 × 10⁻³ m = 3 mm
Answer (b). Convert both nm and mm to metres before dividing. Mixing them is the usual source of a factor-of-1000 error.
3. Grating orders. A grating has 5000 lines per cm. Light of wavelength 500 nm falls on it normally. At what angle is the first-order maximum, and what is the highest order you can see?
N = 5000 per cm = 5 × 10⁵ per m
d = 1/N = 2 × 10⁻⁶ m
first order: sinθ = λ/d = 5 × 10⁻⁷ / 2 × 10⁻⁶ = 0.25 → θ ≈ 14.5°
d/λ = 4, but m = 4 needs sinθ = 1 (θ = 90°), which lies along the grating
highest visible order = 3
This is the grating trap. When d/λ comes out as a whole number, that order sits at 90° and you cannot see it. Round down, and if the result is exact, subtract one.
4. Bragg diffraction. X-rays strike a crystal with atomic spacing 2 × 10⁻¹⁰ m at a glancing angle of 30°. First-order diffraction is observed. What is the wavelength?
(a) 4 × 10⁻¹⁰ m (b) 2 × 10⁻¹⁰ m (c) 1 × 10⁻¹⁰ m (d) 0.5 × 10⁻¹⁰ m
2d sinθ = nλ
λ = 2 × 2 × 10⁻¹⁰ × 0.5 / 1 = 2 × 10⁻¹⁰ m
Answer (b). The angle in Bragg's law is measured from the crystal plane, not from the normal. If a question gives the angle of incidence from the normal, use 90° minus it.
5. Two polarizers. Unpolarized light of intensity I₀ passes through two polarizers whose axes are 60° apart. What intensity comes out?
(a) I₀/2 (b) I₀/4 (c) I₀/8 (d) 3I₀/8
after first polarizer: I₀ / 2
after second: (I₀ / 2) × cos²60° = (I₀ / 2) × ¼ = I₀ / 8
Answer (c). Option (b) forgets the first halving. Option (d) uses sin² instead of cos².
Traps that cost marks
- Coherent means a fixed phase relationship. Same frequency is not enough. Two separate bulbs are never coherent, which is why Young used one source and two slits.
- Central fringe colour. With white light, the central fringe is white and the side fringes are coloured. Path difference is zero at the centre for every wavelength.
- Light entering water. Frequency stays the same. Speed and wavelength both fall by a factor of n. The fringe width in water falls by n too.
- Only transverse waves polarize. Polarization is the evidence that light is transverse. Sound in air cannot be polarized.
- Single-slit minima start at m = 1. The central maximum is twice as wide as the others. In a grating, m = 0 is the central bright line.
- Smaller d spreads the orders. From sinθ = mλ/d, a grating with more lines per metre has a smaller d and throws each order out at a larger angle. It also shows fewer orders in total.
Speed tips for the exam
Treat every fringe-width question as a ratio first. Δy ∝ λL/d, so changing L, d or the medium is a one-line scale.
For gratings, write d in micrometres and λ in micrometres too. d = 2 μm and λ = 0.5 μm give d/λ = 4 at a glance.
Know cos²30° = ¾, cos²45° = ½ and cos²60° = ¼. Every Malus's law question uses one of them.
Interference and beats are the same superposition idea you met in waves and vibrations. Photons and the particle side of light come up in quantum physics.
FAQ
Are gravitational waves in the NET syllabus?
They are part of the first-year chapter title, Physical Optics and Gravitational Waves. Expect concept questions, such as what LIGO measures and that it uses laser interferometry, rather than numericals.
What is the formula for fringe width?
Fringe width = λL/d, where λ is the wavelength, L is the slit-to-screen distance and d is the slit separation. It is the same for bright and dark fringes.
Why can't we see the order where sinθ = 1 in a grating?
That order would leave the grating at 90°, travelling along its surface, so it never reaches the screen. The highest visible order is the largest whole number strictly less than d/λ.
Is physical optics scoring for NET?
Yes, for most students. The question types are narrow and repeat often, so a few timed sets cover most of what you will see.
