(a)
What is the intensity of light exiting the last polarizer?
(a)
Answer to Problem 62P
The intensity of light exiting the last polarizer is
Explanation of Solution
The light is un-polarized at first. When an un-polarized light is passed through a polarizer, its intensity becomes half of the initial.
Write the equation to find the intensity of light from first polarizer.
Here,
Write the equation to find the intensity of light coming from second polarizer.
Here,
Write the equation to find the intensity of light coming from third polarizer.
Here,
Conclusion
Substitute
Substitute
Therefore, The intensity of light exiting the last polarizer is
(b)
What is the intensity of light exiting the last polarizer if the light is incident vertically from left?
(b)
Answer to Problem 62P
The intensity of light exiting the last polarizer is
Explanation of Solution
Here the light has the same polarization as the first ideal polarizer; there will be no change in intensity for light that passes the first polarizer.
Write the equation to find the intensity of light coming from second polarizer.
Write the equation to find the intensity of light coming from third polarizer.
Conclusion:
Substitute
Substitute
Therefore, The intensity of light exiting the last polarizer is
(c)
Can one polarizer be removed from this series of filters so that light incident from the left is not transmitted at all if un-polarized light is incident as in part a? If so, which one should be removed and answer same questions for vertically polarized incident light as in part b.
(c)
Answer to Problem 62P
Yes, polarizer can be removed. In both cases remove the middle polarizer.
Explanation of Solution
In both the cases in part a and part b the light is vertically polarized. The angle of polarization between the first and last polarizers is
Conclusion:
Therefore, yes, polarizer can be removed. In both cases remove the middle polarizer.
(d)
Which polarizer should be removed to maximize the amount of light transmitted in part a?
(d)
Answer to Problem 62P
In case a first polarizer should be removed and in case b last polarizer should be removed.
Explanation of Solution
Consider case a.
Write the equation to find the intensity if the first polarizer is removed.
Write the equation to find the intensity if the last polarizer is removed.
Consider part b.
Write the equation to find the intensity if the first polarizer is removed.
Here,
Write the equation to find the intensity if the last polarizer is removed.
Here,
Conclusion:
Substitute
Substitute
Here for maximum intensity first polarizer should be removed.
Substitute
Substitute
Here for maximum intensity last polarizer shall be removed.
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Chapter 22 Solutions
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