Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 31, Problem 59P
To determine

The optimal number of sheet.

Expert Solution & Answer
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Answer to Problem 59P

The optimal number of sheets is 11 .

Explanation of Solution

Formula used:

The expression for intensity is given by,

  IN+1=I0cos2(π2N)

Calculation:

The intensity for 2% loss is calculated as,

  IN+1=I0(0.98)cos2(π 2N)I N+1I0=(0.98)cos2(π 2N)

For the ideal polarizer,

  IN+1I0=cos2(π2N)

For the real polarizer,

  IN+1I0=(0.98)cos2(π2N)

So, the percent transmission is given by,

  x=(0.98)N

The values of IN+1I0 for different values of N for ideal polarizer, real polarizer and percent transmission is shown in table below,

    For ideal polarizerPercent transmissionReal polarizer
    N

      cos2(π2N)

    (0.98)N

      (0.98)cos2(π2N)

    10.0000.9800.000
    20.2500.9600.240
    30.4220.9410.397
    40.5310.9220.490
    50.6050.9040.547
    60.6600.8860.584
    70.7010.8680.608
    80.7330.8510.624
    90.7590.8340.633
    100.7810.8170.638
    170.8480.7390.626
    180.8570.7240.620
    190.8650.7090.613
    200.8720.6950.606
    210.8780.6810.598
    220.8840.6680.590

Table 1

The graph of intensity of transmitted light as a function of N consider table 1 is shown below,

  Physics for Scientists and Engineers, Chapter 31, Problem 59P

Figure 1

The inspection of the graph gives the optimal number of sheets N is 11 ,

Conclusion:

Therefore, the optimal number of sheets is 11 .

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