An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by which the transmitted beam’s intensity is reduced in the three following cases. (a) Three filters are in the stack, each with its transmission axis at 45.0° relative to the preceding filter. (b) Four filters are in the stack, each with its transmission axis at 30.0° relative to the preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15.0° relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and (c).
(a)
Answer to Problem 38.48P
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)
Answer to Problem 38.48P
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)
Answer to Problem 38.48P
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)
Answer to Problem 38.48P
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 38 Solutions
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