(a)
The fraction by which the transmitted intensity is reduced.
(a)
Answer to Problem 32P
The intensity will be reduced by
Explanation of Solution
Given info: The number of the polarizing filters is
Here,
When an unpolarized light is passed through a polarizing filter intensity is reduced to half. So after passing through the first polarizer the intensity of the light becomes half.
Here,
The angle between the transmission axis of second polarizer and the first polarizer is
Here,
The third polarizing filter and the second polarizing filter has the same
Therefore the final intensity after three polarizing filters is,
Substitute
Substitute
From equation (5), a general formula for the calculation of intensity when light is passed through
Here,
Substitute
Therefore the absorbed intensity is
Conclusion:
Therefore, the fraction by which the intensity is reduced is
(b)
The fraction by which intensity is reduced when
(b)
Answer to Problem 32P
The fraction by which the intensity is reduced is
Explanation of Solution
Given info: The number of filters are
From equation (6) the formula to calculate when there are
Substitute
Therefore the absorbed intensity is
Conclusion:
Therefore, The fraction by which the intensity is reduced is
(c)
The fraction by which intensity is reduced when
(c)
Answer to Problem 32P
The fraction by which the intensity is reduced is
Explanation of Solution
Given info: The number of filters are
From equation (6) the formula to calculate when there are
Substitute
Therefore the absorbed intensity is
Conclusion:
Therefore, the fraction by which the intensity is reduced is
(d)
The comparison between answer of part (a), (b) and (c).
(d)
Answer to Problem 32P
The intensity of light can be increased by increasing the number of stacks of polarizing filters by decreasing the angle between their transmission axis.
Explanation of Solution
From equation (7), (8) and (9), it is evident that, as the number of polarizing filters increased the fraction of absorbed was decreased. For the case of
Conclusion:
Therefore, the intensity of light can be increased by increasing the number of stacks of polarizing filters by decreasing the angle between their transmission axis.
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Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
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