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 Physics · Physics · Oscillations, waves and light. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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
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