A beam of plane polarised light of large cros | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: Intensity $I_0 = 3.3 \, W m^{-2}$,Area $A = 3 	imes 10^{-4} \, m^2$,Angular speed $\omega = 31.4 \, rad/s$.The intensity of light passing

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Given: Intensity $I_0 = 3.3 \, W m^{-2}$,Area $A = 3 	imes 10^{-4} \, m^2$,Angular speed $\omega = 31.4 \, rad/s$.The intensity of light passing through a rotating polariser is given by Malus' Law: $I(t) = I_0 \cos^2(\omega t)$.The power transmitted at any instant is $P(t) = I(t) 	imes A = I_0 A \cos^2(\omega t)$.The energy $E$ transmitted in one revolution (time period $T = \frac{2\pi}{\omega}$) is the integral of power over the period:$E = \int_{0}^{T} P(t) dt = \int_{0}^{2\pi/\omega} I_0 A \cos^2(\omega t) dt$.Using the average value of $\cos^2(	heta)$ over a full cycle,which is $\frac{1}{2}$:$E = I_0 A 	imes \frac{1}{2} 	imes T = I_0 A 	imes \frac{1}{2} 	imes \frac{2\pi}{\omega} = \frac{I_0 A \pi}{\omega}$.Substituting the values:$E = \frac{3.3 	imes 3 	imes 10^{-4} 	imes 3.14}{31.4} = \frac{3.3 	imes 3 	imes 10^{-4} 	imes 3.14}{10 	imes 3.14} = \frac{9.9 	imes 10^{-4}}{10} = 0.99 	imes 10^{-4} \, J$.Rounding to the nearest integer,$E \approx 1 	imes 10^{-4} \, J$.

$A$. Angle of reflection	$(i)$ $2 \sin^{-1} \left(\sqrt{\frac{2}{3}}\right)$
$B$. Angle of refraction	$(ii)$ $\sin^{-1} \left(\sqrt{\frac{2}{3}}\right) - \sin^{-1} \left(\frac{1}{\sqrt{3}}\right)$
$C$. Angle between incident and completely polarised light	$(iii)$ $\sin^{-1} \left(\frac{1}{\sqrt{3}}\right)$
$D$. Angle of deviation of the incident ray	$(iv)$ $\cos^{-1} \left(\frac{1}{\sqrt{3}}\right)$

Similar Questions

An optically active compound:

Two polarizers are oriented with their principal planes making an angle of $60^{\circ}$ with each other. The percentage of incident unpolarized light which passes through the system is: (in $\%$)

It is possible to distinguish between the transverse and longitudinal waves by studying the property of

Vedclass Test Series

Exam Paper Generator

Online Exam Module