Unit 15: Physical Optics — Short Questions

Yes. Huygens' Principle is a general geometrical construction for any wave: every point on a wavefront acts as a source of secondary wavelets that spread out with the speed of the wave, and the new wavefront is the envelope (tangent surface) of these wavelets. Since this idea depends only on the wave nature of the disturbance and not on what is waving, it applies equally to sound waves and water (ripple-tank) waves, which also form wavefronts and travel at a definite speed, just as it applies to light.

A soap bubble's film is extremely thin (comparable to the wavelength of visible light), so the path difference 2t between light reflected from its front and back surfaces is only a few wavelengths, giving a clear, visible pattern of constructive and destructive interference (coloured bands) for ordinary light. A window pane or windscreen is far thicker (millimetres), so the path difference between the front- and back-surface reflections is enormous compared to the wavelength; the condition for constructive/destructive interference changes many times within the small range of wavelengths and angles reaching the eye, washing the pattern out, so no distinct fringes are seen.

The wavelength of light is shorter in water than in air (λ_water = λ_air/n, where n is the refractive index of water, about 1.33). Since fringe spacing Δy = λL/d, a smaller λ gives a smaller Δy. So the fringes would move closer together (fringe width decreases), though their number and overall pattern shape remain the same.

Similarities both arrangements need two coherent sources with a constant phase difference, and both produce a pattern of constructive (loud/bright) and destructive (quiet/dark) regions following the same path-difference condition, dsinθ = mλ for maxima. Differences: for sound, coherence is obtained by connecting two loudspeakers to the same signal generator, and the slit/gap separation can be centimetres because sound wavelengths are large; the pattern is detected with a probe/microphone as loudness. For light, coherence is obtained by splitting one laser beam through two very closely spaced (fraction of a millimetre) slits, because the wavelength of light is extremely small, and the pattern is detected visually or on a screen as bright and dark fringes.

(a) Many slits: the principal maxima stay at the same angular positions as for two slits but become much narrower and sharper, so the angular position (and hence the wavelength) can be measured to very high precision, giving a grating higher resolving power. (b) Narrow slits: each slit diffracts (spreads) light over a wide angular range, so many orders remain bright enough to be seen, giving a broad, useful spectrum. (c) Closely spaced slits: a smaller grating spacing d gives a larger angle θ for a given order (sinθ = nλ/d), spreading the orders further apart on the screen, which makes it easier to resolve and measure closely spaced wavelengths.

Since maxima occur at d sinθ = nλ and sinθ cannot exceed 1, the highest possible order is n_max = d/λ. The number of visible orders can therefore be increased by using a grating with larger spacing d (fewer lines per millimetre) or by using light of shorter wavelength λ.

Blue light has a shorter wavelength than red light. Since d sinθ = nλ, for the same grating spacing d and same order n, a smaller λ gives a smaller θ. So all the diffraction maxima (first order, second order, etc.) move closer to the central maximum. Also, because n_max = d/λ, more higher orders become visible with blue light than with red light.

At the point of contact between the lens and the glass plate, the air film thickness t is zero, so the geometrical path difference 2t is zero. However, one of the two reflected waves undergoes an extra half-cycle (π) phase shift on reflection, so the two waves meeting at the centre are effectively out of phase by half a wavelength even though their path difference is zero. This causes destructive interference at the centre, giving a dark central spot instead of a bright one.