#wave behavior

Polarization and Malus Law

Why does light exhibit polarization only in specific directions when passing through a polaroid?

**Two polaroids** with pass-axes perpendicular intensity zero because second blocks component, with 45° intensity I₀/4 if initial after first I₀, if initial unpolarized I₀, after first I₀/2 then after second at 45° I₀/4. Three polaroids first and third crossed 90°, middle at 45° maximum transmission because middle rotates polarization, I after first I₀/2, after middle at 45° I₀/4, after third at 45° to middle I₀/4×cos²45°= I₀/8, non-zero, maximum when middle 45°. The polaroid aligns the electric field along its pass-axis, absorbing components in other directions, restricting polarization to th

Ref: NCERT > Physics Book > Wave Optics > Polarization and Malus Law

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Wavefront and Huygens Principle

What happens to the refracted wavefront when light enters a medium where its speed increases?

**Huygens principle** predicts shape of wavefront after propagation, for point source close spherical, far plane, after reflection from plane mirror spherical wave becomes spherical with centre mirrored, plane wave remains plane but direction changes angle of incidence equals reflection, after passing through thin prism plane wavefront tilts due to different path. When speed increases (e.g., from glass to air), the refracted wavefront bends away from the normal. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Bends

Ref: NCERT > Physics Book > Wave Optics > Wavefront and Huygens Principle

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Refraction, Refractive Index and Critical Angle

Why does total internal reflection occur only when light travels from a denser to a rarer medium?

**Refractive index** n = c/v, c=3×10⁸ m/s vacuum, v speed in medium, for v=2.25×10⁸ m/s n=3/2.25=1.33, for v=1.8×10⁸ n=1.67, for n=1.3 v=3×10⁸/1.3=2.31×10⁸ m/s, for n=1.6 v=1.875×10⁸ m/s, for n=1.2 λ_medium = λ_vacuum/n =600/1.2=500 nm, for n=1.75 λ=700/1.75=400 nm, for n=1.5 λ=750/1.5=500 nm, wavelength in medium λ' = λ/n. In a denser medium, the critical angle exists due to a lower speed, beyond which refraction cannot occur, leading to reflection; this doesn’t happen in the reverse direction. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and

Ref: NCERT > Physics Book > Wave Optics > Refraction, Refractive Index and Critical Angle

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Production of EM Waves and Hertz Experiment

What explains the ability of electromagnetic waves to exhibit polarization?

**Production of EM waves** requires accelerated charge, oscillating LC circuit produces changing E and B, antenna radiates when charge accelerates, frequency determined by L and C, f=1/(2π√(LC)). Hertz used spark gap with inductor and capacitor, produced ~10⁸ Hz radio waves, detected with loop, confirmed transverse nature, reflection, refraction, polarization, speed c. Electromagnetic waves are transverse, meaning their electric and magnetic fields oscillate perpendicular to the direction of propagation, allowing the orientation of these fields to be manipulated for polarization. Using c = fλ,

Ref: NCERT > Physics Book > Electromagnetic Waves > Production of EM Waves and Hertz Experiment

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Stationary Waves and Standing Waves in Strings

What is the key difference between a progressive wave and a standing wave?

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. A progressive wave transfers energy through the medium as it propagates, while a standing wave has fixed nodes and antinodes with no net energy transfer, only oscillation. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Energy transfer, illustrating freque

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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Wave Equation and Displacement Relation

What happens to a transverse wave when it reflects off a fixed end of a string?

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. At a fixed end, the displacement must be zero, requiring the reflected wave to be out of phase by π radians (inverted) to cancel the incident wave at the boundary. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It reflects with a phase change of π radians, illustrating frequency-length-speed interdependence and quanti

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Wave Equation and Displacement Relation

Which characteristic of a wave remains constant when it travels from one medium to another with different properties?

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. When a wave crosses a boundary between media, its speed and wavelength change due to differing medium properties, but frequency remains constant as it is determined by the source. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Frequency, illustrating frequency-length-speed interdependence and quantization by boundarie

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Stationary Waves and Standing Waves in Strings

Which statement best describes the energy in a standing wave?

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. In a standing wave, energy oscillates between kinetic (at antinodes) and potential (at nodes) forms but does not propagate, remaining trapped within the medium. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It does not oscillate, illustrating frequency-l

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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