Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 36, Problem 22P

(a)

To determine

The wavelength and the color of the light in the visible spectrum most strongly reflected.

(a)

Expert Solution
Check Mark

Answer to Problem 22P

The value of wavelength of the light for m=1 is 541.33nm and the colour of the light in the visible spectrum most strongly reflected is green.

Explanation of Solution

Given Information: The refractive index of the oil film is 1.45 , thickness of the film is 280nm .

It is given that an oil film floating on water is illuminated by white light at normal incidence as shown in figure given below.

Physics for Scientists and Engineers with Modern Physics, Chapter 36, Problem 22P

Figure (1)

For most strongly reflected waves:

Write the expression for the constructive interference in thin film.

2μoilt=(m+12)λ (1)

Here,

μoil is the refractive index of the oil film.

λ is the value of wavelength of the light.

t is the thickness of the film.

m is the order number.

From equation (1), formula to calculate the value of wavelength of the light is,

λ=2μoilt(m+12) (2)

From equation (2), formula to calculate the value of wavelength of the light for m=0 is,

λ0=2μoilt(m+12) (3)

Here,

λ0 is the value of wavelength of the light for m=0 .

Substitute 0 for m , 1.45 for μoil , 280nm for t in equation (3) to find λ0 ,

λ0=2×1.45×280nm(0+12)=1624nm

The range for the wavelength of the visible light is 390nm to 700nm .

Thus, the value of wavelength of the light for m=0 is 1624nm and the colour of the light in the invisible spectrum is infared.

From equation (2), formula to calculate the value of wavelength of the light for m=1 is,

λ1=2μoilt(m+12) (4)

Here,

λ1 is the value of wavelength of the light for m=1 .

Substitute 1 for m , 1.45 for μoil , 280nm for t in equation (4) to find λ1 ,

λ1=2×1.45×280nm(1+12)=541.33nm

Thus, the value of wavelength of the light for m=1 is 541.33nm and the colour of the light in the visible spectrum is green.

From equation (2), formula to calculate the value of wavelength of the light for m=2 is,

λ2=2μoilt(m+12) (4)

Here,

λ2 is the value of wavelength of the light for m=2 .

Substitute 1 for m , 1.45 for μoil , 280nm for t in equation (4) to find λ2 ,

λ2=2×1.45×280nm(2+12)=324.8nm325nm

Thus, the value of wavelength of the light for m=2 is 325nm and the colour of the light in the invisible spectrum is ultraviolet.

Conclusion:

Therefore, the value of wavelength of the light for m=1 is 541.33nm and the colour of the light in the visible spectrum most strongly reflected is green.

(b)

To determine

The wavelength and the color of the light in the spectrum most strongly transmitted.

(b)

Expert Solution
Check Mark

Answer to Problem 22P

The value of wavelength of the light for m=1 is 271nm and the colour of the light in the visible spectrum most strongly transmitted is violet.

Explanation of Solution

Given Information: The refractive index of the oil film is 1.45 , thickness of the film is 280nm .

For most strongly transmitted waves:

Write the expression for the destructive interference in thin film.

2μoilt=mλ (5)

From equation (5), formula to calculate the value of wavelength of the light is,

λ=2μoiltm (6)

From equation (6), formula to calculate the value of wavelength of the light for m=1 is,

λ0=2μoiltm (7)

Here,

λ0 is the value of wavelength of the light for m=1 .

Substitute 1 for m , 1.45 for μoil , 280nm for t in equation (7) to find λ0 ,

λ0=2×1.45×280nm1=812nm

Thus, the value of wavelength of the light for m=1 is 812nm and the colour of the light in the invisible spectrum is infared.

From equation (6), formula to calculate the value of wavelength of the light for m=2 is,

λ1=2μoiltm (8)

Here,

λ1 is the value of wavelength of the light for m=2 .

Substitute 2 for m , 1.45 for μoil , 280nm for t in equation (8) to find λ1 ,

λ1=2×1.45×280nm2=406nm

Thus, the value of wavelength of the light for m=2 is 406nm and the colour of the light in the visible spectrum is violet.

From equation (6), formula to calculate the value of wavelength of the light for m=3 is,

λ2=2μoiltm (9)

Here,

λ2 is the value of wavelength of the light for m=3 .

Substitute 3 for m , 1.45 for μoil , 280nm for t in equation (9) to find λ2 ,

λ2=2×1.45×280nm3=270.666nm271nm

Thus, the value of wavelength of the light for m=3 is 271nm and the colour of the light in the invisible spectrum is ultraviolet.

Conclusion:

Therefore, the value of wavelength of the light for m=1 is 271nm and the colour of the light in the visible spectrum most strongly transmitted is violet.

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