#Malus law

What causes the intensity to vary when a second polaroid is rotated in front of another polaroid through which unpolariz

**Convex lens focusing** plane wave into point because lens introduces phase delay proportional to thickness, converting plane wavefront to spherical converging to focal point, property ensures rays parallel to axis meet at focus, spherical aberration minimized for paraxial rays, lensmaker's formula determines focal length. The first polaroid polarizes the light linearly, and the second allows only the component of the electric field aligned with its pass-axis, varying with the angle via Malus’ law. 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

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Optical Phenomena and Applications

What causes the intensity of light to vary sinusoidally with angle when passing through two polaroids?

**Polarization requires transverse waves** because only transverse can have orientation perpendicular to propagation, longitudinal cannot be polarized, wave theory requires light transverse to explain polarization, polaroids transmit only component along pass-axis, unpolarized has random transverse orientations, after polaroid polarized. The intensity follows Malus’ law, where it varies as the square of the cosine of the angle between the polaroids’ axes, producing a sinusoidal pattern. 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)

Ref: NCERT > Physics Book > Wave Optics > Optical Phenomena and Applications

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Optical Phenomena and Applications

What is the intensity of light after passing through two polaroids with pass-axes at \( 45^\circ \), if the initial unpo

**Incoherent sources** intensity adds I = I₁+I₂, no interference pattern because phase random, two independent sources cannot produce stable interference because phase difference fluctuates rapidly, coherent sources required with constant phase, laser coherent, visibility of fringes requires coherence, degree of coherence determines contrast. After the first polaroid, I = (I₀/2) . After the second at 45° , I = (I₀/2) cos² 45° = (I₀/2) × (1/2) = (I₀/4) . 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 (I₀/4),

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Polarization and Malus Law

What is the intensity of light after passing through three polaroids, with the first and third crossed and the second at

**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°. After the first polaroid, I = (I₀/2) . After the second at 45° , I = (I₀/2) cos² 45° = (I₀/4) . Third at 90° - 45° = 45° to second,