Question 124: Wave Optics

Question

A beam of plane polarised light of large
cross-sectional area and uniform intensity
of 3.3 Wm
-2
falls normally on a
polariser (cross sectional area 3 $$ 	imes $$ 10
-4
m
2
) which
rotates about its axis with an angular speed
of 31.4 rad/s. The energy of light passing through
the polariser per revolution, is close to :

Accepted Answer

Intensity, I = 3.3 Wm
Ã¢ÂÂ3
Area, A = 3 ÃÂ 10
Ã¢ÂÂ4
m
2
Angular speed, $$\omega $$ = 31.4 rad/s
$$I = {I_0}{\cos ^2}(\omega t)$$
$$ \Rightarrow {I_{av}} = {{{I_0}} \over 2}$$
$$ \because $$ $$\left\langle {{{\cos }^2}	heta } ightangle $$ = $${1 \over 2}$$, in one time period
$$ 	herefore $$ $$E = {{{I_0}} \over 2} 	imes A 	imes (\Delta t)$$
and $$\Delta t = {{2\pi } \over \omega } = {{2 	imes 3.14} \over {31.4}} = {1 \over 5}s$$
$$ 	herefore $$ $$E = {{3.3} \over 2} 	imes 3 	imes {10^{ - 4}} 	imes {1 \over 5} = 1 	imes {10^{ - 4}}\,J$$

Answer

1.0 $$ 	imes $$ 10
-5
J

Answer

1.0 $$ 	imes $$ 10
-4
J

Answer

1.5 $$ 	imes $$ 10
-4
J

Answer

5.0 $$ 	imes $$ 10
-4
J

Wave Optics

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