What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

State Huygens' principle.

Every point on a wavefront acts as a source of secondary spherical wavelets; their envelope gives the new wavefront.

What is the condition for constructive interference?

Path difference equals an integral multiple of the wavelength, \(\Delta=n\lambda\).

Give the fringe width in Young's experiment.

\(\beta=\dfrac{\lambda D}{d}\), the spacing between successive bright fringes.

Why are two independent bulbs not coherent?

They emit light with rapidly and randomly changing phase, so no stable interference pattern forms.

Where does the first diffraction minimum occur for a single slit?

At \(a\sin\theta=\lambda\), where \(a\) is the slit width.

How does diffraction limit a microscope's resolution?

The finite aperture spreads each point into a disc, setting a minimum resolvable separation.

What does polarisation tell us about light?

That light is a transverse wave, since only transverse waves can be polarised.

Transmitted intensity through a polariser is \(I=I_0\cos^2\theta\), \(\theta\) being the angle between axis and polarisation.

Define Brewster's angle.

The angle of incidence at which reflected light is completely plane-polarised, with \(\tan i_B=n\).

What happens to fringe width if the whole apparatus is immersed in water?

It decreases, since the wavelength of light reduces in the denser medium.

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Wave Optics — Class 12 Physics

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Chapter 2: Wave Optics

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Summary

Wave optics explains phenomena that ray optics cannot, by treating light as a wave. Huygens' principle, in which every point on a wavefront is a source of secondary wavelets, derives the laws of reflection and refraction. When two coherent waves overlap they interfere; Young's double-slit experiment produces alternating bright and dark fringes of spacing \(\beta=\dfrac{\lambda D}{d}\), bright where the path difference is an integral multiple of \(\lambda\) and dark where it is an odd multiple of \(\lambda/2\). Coherence—a constant phase relationship—is essential for stable fringes. Diffraction, the bending of light around obstacles and slits, gives a central bright maximum flanked by weaker minima, with the first minimum at \(a\sin\theta=\lambda\); this sets the ultimate resolution limit of optical instruments. Polarisation reveals the transverse nature of light: unpolarised light becomes plane-polarised on passing through a Polaroid, obeying Malus' law \(I=I_0\cos^2\theta\), and on reflection at Brewster's angle \(\tan i_B=n\). Together these effects confirm light's wave character and underpin modern optical technology.

Huygens' principle and wavefrontsInterference and Young's experimentCoherence and path differenceDiffraction at a single slitResolving powerPolarisation, Malus' and Brewster's laws

Key terms

Wavefront

Surface of constant phase; every point is a source of secondary wavelets.

Coherence

Constant phase relationship between sources, needed for stable interference.

Fringe width

Spacing between adjacent bright (or dark) fringes, \(\beta=\lambda D/d\).

Diffraction

Bending and spreading of waves around obstacles and through slits.

Polarisation

Restriction of light vibrations to one plane, showing light is transverse.

Brewster's angle

Angle of incidence \(i_B\) giving fully polarised reflected light, \(\tan i_B=n\).

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Practice quiz

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Class 12 Physics — Wave Optics (Practice Quiz)

10 Qs · ~10 min