Light of wavelength 500 nm falls normally on a grating with 5000 lines per cm. At what angle is the second-order maximum seen?
- d = 1/5000 cm = 2 × 10−4 cm = 2 × 10−6 m.
- sin θ = nλ/d = (2 × 500 × 10−9)/(2 × 10−6) = 0.50.
- θ = 30°.
Answer: 30°
Physical optics and optical instruments
NUST NET (Engineering) · Physics · Oscillations, waves and light. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
The idea
Light is a wave, so it shows interference and diffraction. Where two coherent beams meet with a path difference of a whole number of wavelengths they give a bright fringe; half a wavelength extra gives a dark one. Young's double slit and the diffraction grating both use this to measure wavelength.
Polarisation means the vibrations are limited to one plane. It can only happen to transverse waves, so it proves light is transverse. Light reflected from water or a road is partly polarised.
Optical instruments are judged by magnifying power (how much larger the image looks) and resolving power (how fine a detail can be seen as separate).
Rules to remember
- Young's double slit: fringe spacing = λL/d (d = slit separation, L = distance to screen)
- Bright fringe m at y = mλL/d (path difference mλ); dark fringe at y = (m + ½)λL/d
- Diffraction grating: d sin θ = nλ, with d = 1/N (N = lines per metre); highest order n ≤ d/λ
- Unpolarised light through an ideal polariser: intensity falls to half; two crossed polarisers pass nothing
- Simple magnifier: M = 1 + d/f (d = 25 cm); compound microscope: M = Mobjective × Meyepiece
- Astronomical telescope in normal adjustment: M = fo/fe, length = fo + fe
- Smallest angle resolved by a lens of diameter D: αmin = 1.22λ/D (radians); grating resolving power λ/Δλ = N × m (here N = total number of lines lit, m = order)
Common mistake
Putting the number of lines per centimetre straight into d sin θ = nλ. First find the spacing d = 1/N and change it to metres: 5000 lines per cm gives d = 2 × 10−6 m.
Worked example
Practice questions
Try each one, then open the answer.
1. Polaroid sunglasses cut down the glare of sunlight reflected from a wet road because the reflected light is
- Aunpolarized and very bright
- Bpartially plane-polarized, and the Polaroid blocks most of it
- Cof shorter wavelength than direct sunlight
- Dcoherent, so it cancels itself by interference
Show answer
Answer: B. Light reflected from a horizontal surface such as water is partially plane-polarized, vibrating mostly parallel to the surface. Polaroid lenses with a vertical transmission axis block most of that light.
2. In Young's double-slit experiment the fringe spacing is 0.60 mm with light of wavelength 600 nm. Light of wavelength 400 nm is used instead, with nothing else changed. The new fringe spacing is
- A0.90 mm
- B0.60 mm
- C0.40 mm
- D0.27 mm
Show answer
Answer: C. Fringe spacing Δy = λL/d is proportional to λ, so it becomes 0.60 × 400/600 = 0.40 mm. 0.90 mm uses the ratio upside down: shorter wavelengths give closer fringes.
3. Unpolarized light of intensity I0 falls on an ideal polarizer (Polaroid sheet). The intensity of the light that passes through is
- AI0
- BI0/4
- Czero
- DI0/2
Show answer
Answer: D. The polarizer passes only the vibrations along its transmission axis. Averaged over all directions of vibration this is half the intensity, I0/2, and the light that emerges is plane-polarized.
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