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Unpolarized light of intensity 32Wm^(-2) passes through three polarizers such that the transmission axis of the last polarizer is crossed with the first. If the intensity of the emerging light is 3 Wm^(-2), what is the angle between the transmission axes of the first two polarizers? At what ange will the transmitted intensity be maximum? |
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Answer» Solution :If `theta` is the angle between the transmission axes of first polaroid `P_1` and second `P_2` while `phi` between the transmission axes of second polaroid `P_2` and third `P_3`, then according to given PROBLEM. `theta+ phi= 90^(@)" or "phi= (90^(@)-theta)""".........."(i)` Now if `I_(0)` is the intensity of unpolarized LIGHT incident on polaroid `P_(1)`, the intensity of light transmitted through it, `I_(1)= (1)/(2)I_(0)= (1)/(2)(32)= 16(W)/(m^2)"""............"(ii)` Now as angle between transmission axes of polaroids `P_1" and "P_(2)` is `theta P_(2)" and "P_(3)` is `phi`, light transmitted through `P_3` will be `I_(3)= (I_0)/(2) cos^(2) theta* cos^(2) 90-theta= (I_0)/(8)sin^(2) 2theta` According to given proble, `I_(3)= 3 W"/"m^(2)` So, `4(sin 2 theta)^(2)= 3` `i.e., sin 2theta= (SQRT(3)"/"2)" or "2theta= 60^(@) i.e., theta= 30^(@)`. |
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