Correct answer with work are needed The above diagram represents a series of pol
ID: 1997986 • Letter: C
Question
Correct answer with work are needed The above diagram represents a series of polarizers (six are shown, but it could be fewer or more) each rotated through the same angle theta = N with respect to the previous polarizer. Initially polarized light shines from the left. How many polarizers are necessary to get the final intensity of the light emerging on the right to be under 1/100 (that is. 1%) of the initial Intensity of the un polarized light? Answer: polarizers How many polarizers are necessary to get the final intensity of the light emerging on the right to be under 1/1000 (that is, 0.1%) of the initial intensity of the un polarized light?Explanation / Answer
(a).
Let the intensity of the unpolarized light be I
Intensity of the light after first polarizer I1 = I/2 = 0.5 I
Intensity of the light after second polarizer I2= I1 cos 2 37.9
I2 = 0.5I cos 2 37.9
Intensity of the light after third polarizer I3 = I2 cos 2 37.9
= 0.5 I [cos 2 37.9] 2
Intensity of the light after n th polarizer In = 1 % of I
= 0.01 I
From above In = 0.5 I [cos 2 37.9] n-1
0.5 I [cos 2 37.9] n-1 = 0.01 I
0.5 [cos 2 37.9] n-1= 0.01
[cos 2 37.9] n-1 = 0.02
ln {[cos 2 37.9] n-1 } = ln 0.02
(n-1) ln {[cos 2 37.9]} = -3.912
(n-1) ln(0.6226) = -3.912
(n-1) (-0.4737) = -3.912
n-1 = 8.25
n = 9.25
So, answer is 10
(b).
Let the intensity of the unpolarized light be I
Intensity of the light after first polarizer I1 = I/2 = 0.5 I
Intensity of the light after second polarizer I2= I1 cos 2 37.9
I2 = 0.5I cos 2 37.9
Intensity of the light after third polarizer I3 = I2 cos 2 37.9
= 0.5 I [cos 2 37.9] 2
Intensity of the light after n th polarizer In = 0.1 % of I
= 0.001 I
From above In = 0.5 I [cos 2 37.9] n-1
0.5 I [cos 2 37.9] n-1 = 0.001 I
0.5 [cos 2 37.9] n-1= 0.001
[cos 2 37.9] n-1 = 0.002
ln {[cos 2 37.9] n-1 } = ln 0.002
(n-1) ln {[cos 2 37.9]} = -6.214
(n-1) ln(0.6226) = -6.214
(n-1) (-0.4737) = -6.214
n-1 = 13.11
n = 14.11
So, answer is 15