Q. 67 Scientists are testing a transpa... [FREE SOLUTION]

Chapter 17: Q. 67 (page 486)

Scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as n = 30.0 nm1/2 /l1/2, where l is in nm. If a 295-nm-thick coating is placed on glass 1n = 1.502 for what visible wavelengths will the reflected light have maximum constructive interference?

Short Answer

Expert verified

Here, $位_{c} = 679.18 n m 位_{c} = 427.85 m$

Step by step solution

Understanding the constructive interference

Constructive interference occurs when the maxima of two waves add together so that the amplitude of the resulting wave is equal to the sum of the individual amplitudes

Processing of the equation

Here, $d = 295 m$

Thus, role="math" localid="1649154544207" $n = \frac{30 n m^{1 / 2}}{位^{1 / 2}}$

The wavelength is $位_{c} = \frac{2 n d}{m} m = 1, 2, 3 . . .$

The n= $n = \frac{30 n m^{1 / 2}}{位^{1 / 2}}$ the equation is

role="math" localid="1649154803634" $位_{c} = \frac{2 d}{m} 路 \frac{30 n m^{1 / 2}}{位^{1 / 2}} {位_{c}}^{3 / 2} = \frac{d 60 n m^{1 / 2}}{m} 位_{c} = \sqrt[3]{\frac{d^{2} 路 3600 n m}{m}}$

Thus, the solution to the equation is 5

for m=1 , role="math" localid="1649154869717" $位_{c} = \sqrt[3]{\frac{295^{2} 路 3600 n m}{m}} 位_{c} = 679.18 n m$

for m=2, role="math" localid="1649155019072" $位_{c} = \sqrt[3]{\frac{295^{2} 路 3600 n m}{2}} 位_{c} = 679.18 n m$

For m=3, $位_{c} = \sqrt[3]{\frac{295^{2} 路 3600 n m}{3}} 位 = 326 . 51 n m$

Thus, the interference range in 360 to 700 nanometers is 679.18 nm and 427.89 nm.

Thus,role="math" localid="1649155157302" $位_{c} = 679.18 n m 位_{c} = 427.85 n m$

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Short Answer

Step by step solution

Understanding the constructive interference

Processing of the equation

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