(a) What is plane polarised light? Two polaroids are placed at 90° to each other and the transmitted intensity is zero. What happens when one more polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third polaroid?
(b) If a light beam shows no intensity variation when transmitted through a polaroid which is rotated, does it mean that the light is unpolarized? Explain briefly.

Solution

(a) In plane polarized light, electric field E oscillates back and fourth in one plane perpendicular to the direction of the propagation of light.
The intensity of polarised light through a polarizer at an angle of ө, is given by

I = I_{0} \cos^{2} θ

.
If there are N polaroids placed in between the polarizer and analyzer with equal successive angular separation, then the overall intensity at the analyzer is given by,

I = I_{0} {(\cos \frac{π}{2 N})}^{2 N}

Hence, the intensity of the polarised light coming out from the analyzer is,

I = I_{0} {(\cos \frac{π}{4})}^{2 \times 2} = I_{0} (\cos 45 °)^{4} = \frac{I_{0}}{{(\sqrt{2})}^{4}} = \frac{I_{0}}{4}

According to law of Malus, when a beam of completely plane polarized light is incident on an analyzer, the resultant intensity of light (I₀) transmitted from the analyzer varies directly as the square of the cosine of the angle (ө) between planes of transmission of analyzer and polarizer.

i.e., I = I₀cos²ө.

The variation of intensity of transmitted light with rotating angle is given.

(b) Yes, if a light beam shows no variation when transmitted through a polaroid which is rotated, this means that light is unpolarized. If an unpolarized light from an ordinary source passes through a polaroid sheet P₁, it is observed that its intensity is reduced by half. Rotating P₁ has no effect on the transmitted beam and transmitted intensity remains constant. Now, let an identical piece of polaroid P₂ be placed before P₁. The light from the lamp is reduced in intensity on passing through P₂ alone. In one position, the intensity transmitted by P₂ is nearly zero. When turned by 90° from this position, P₁transmits nearly the full intensity emerging from P₂.

Some More Questions From Wave Optics Chapter

Let us list some of the factors which could possibly influence the speed of wave propagation:
(i) nature of source.
(ii) direction of propagation.
(iii) motion of source and/or observer.
(iv) wave length.
(v) intensity of the wave.
On which of these factors, if any, does
(a) the speed of light in vacuum,
(b) the speed of light in a medium (say, the glass or water) depend?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations:
(i) source at rest; observer moving, and
(ii) source moving; observer at rest.
The exact Doppler formulas for the case of light wave in vacuum, are however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

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