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Show that when the unpolarized light passe through polariser then the intensity emerging light is half that of the intensity the incident light. |
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Answer» Solution :If the intensity of light on the POLARISER is I then the intensity of emergent light (from Malu law) is `I=I_(0)cos^(2)theta` where `theta` is an angle BETWEE pass-axis of both polaroid. When unpolarized light incident on a polaroid the intensity of emerging light is equal to th average intensity between `theta=0` to `2pi`. `:.` Average intensity, `ltIgt""=I_(0)ltcos^(2)thetagt` `=I_(0)int_(0)^(2pi)(cos^(2)theta)/(2pi)d""theta` `=(I_(0))/(2pi)int_(0)^(2pi)[(1+cos2theta)/(2)]d"theta` `(I_(0))/(2pi){[theta]_(0)^(2pi)+[(sin2theta)/(2)]_(theta)^(2pi)}` `=(I_(0))/(4pi){(2pi-0)+(sin4pi-sin0)/(2)}` `=(I_(0))/(4pi){(2pi+0)-0}` `=(I_(0))/(4pi)xx2pi` `=(I_(0))/(2)` Hence, the intensity of emerging light is half that of the intensity of the incident light that means 50%. |
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