EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100546310
Author: Jewett
Publisher: CENGAGE L
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Chapter 37, Problem 37.18P

In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) θ = 0.500° and (b) y = 5.00 mm. (c) What is the value of θ for which the phase difference is 0.333 rad? (d) What is the value of θ for which the path difference is λ/4?

Figure P36.10

Chapter 37, Problem 37.18P, In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is

(a)

Expert Solution
Check Mark
To determine
The phase difference between the two waves fronts arriving at P when θ=0.500° .

Answer to Problem 37.18P

The phase difference between the two waves fronts arriving at P when θ=0.500° is 13.2radian

Explanation of Solution

Given info:  The separation between the slits is 0.120mm and the distance between the slit and screen is 1.20m and wavelength of light is 500nm .

The given diagram is shown below.

EBK PHYSICS FOR SCIENTISTS AND ENGINEER, Chapter 37, Problem 37.18P

Figure 1

The formula to calculate the phase difference is,

ϕ=2πλdsinθ

Here,

λ is the wavelength.

d is the separation between the slits.

θ is the angle between the point P and horizontal.

Substitute 0.120mm for d , 0.500° for θ , 500nm for λ , in the above formula as,

ϕ=2πλdsinθ=2π(500nm×109m1nm)(.120mm×103m1mm)sin(0.500°)=13.2radian

Conclusion:

Therefore, the phase difference between the two waves fronts arriving at P when θ=0.500° is 13.2radian

(b)

Expert Solution
Check Mark
To determine
The phase difference between the two waves fronts arriving at P when y=5.00mm .

Answer to Problem 37.18P

The phase difference between the two waves fronts arriving at P when y=5.00mm is 6.28radian .

Explanation of Solution

Given info:  The separation between the slits is 0.120mm and the distance between the slit and screen is 1.20m and wavelength of light is 6.28radian .

The formula to calculate the phase difference is,

ϕ=2πλdsinθ

Here,

λ is the wavelength.

d is the separation between the slits.

θ is the angle between the point P and horizontal.

From the right angle triangle sinθ is

sinθ=perpendicularhypotenuse=yL

Here,

y is the distance from O to P .

L is the distance between slit and screen.

Substitute yL for  sinθ in the above formula as,

ϕ=2πλdsinθ=2πλd(yL)

Substitute 0.120mm for d , 500nm for λ , 1.20m for L , 5.00mm for y in the above formula as,

ϕ=2πλdsinθ=2π(500nm×109m1nm)(.120mm×103m1mm)(5.00mm×10-3m1mm1.20m)=6.28radian

Conclusion:

Therefore, the phase difference between the two waves fronts arriving at P when y=5.00mm is 6.28radian

(c)

Expert Solution
Check Mark
To determine
The value of θ for which the path difference is λ4 .

Answer to Problem 37.18P

The value of θ for which the path difference is λ4 is 1.27×102degree .

Explanation of Solution

Given info:  The separation between the slits is 0.120mm and the distance between the slit and screen is 1.20m and wavelength of light is 6.28radian , phase difference is 0.33radian

The formula to calculate the phase difference is,

ϕ=2πλdsinθ

Here,

λ is the wavelength.

d is the separation between the slits.

θ is the angle between the point P and horizontal.

Rearrange the above formula to find θ is,

ϕ=2πλdsinθsinθ=λϕ2πdθ=sin1(λϕ2πd)

Substitute 0.120mm for d , 500nm for λ , 0.33radian for ϕ in the above formula as,

θ=sin1(λϕ2πd)=sin1(500nm×109mm1mm(0.33radian)2π(0.120mm×103m1mm))=1.27×102degree

Conclusion:

Therefore, the value of θ is 1.27×102degree .

(d)

Expert Solution
Check Mark
To determine
The value of θ

Answer to Problem 37.18P

The value of θ is 5.97×102degree .

Explanation of Solution

Given info:  The separation between the slits is 0.120mm and the distance between the slit and screen is 1.20m and wavelength of light is 6.28radian , path difference is λ4

The formula to calculate the phase difference is,

ϕ=2πλdsinθ (1)

Here,

λ is the wavelength.

d is the separation between the slits.

θ is the angle between the point P and horizontal.

The path difference is λ4 as,

dsinθ=λ4

Substitute λ4 for dsinθ in the above formula as,

ϕ=2πλdsinθ=2πλ(λ4)=π2

Rearrange the equation (1) to find θ as,

θ=sin1(λϕ2πd)

Substitute 0.120mm for d , 500nm for λ , π2 for ϕ in the above formula as,

θ=sin1(λ(π2)2πd)=sin1(λ4d)=sin1(500nm×109mm1mm4(0.120mm×103m1mm))=5.97×102degree

Conclusion:

Therefore, the value of θ is. 5.97×102degree .

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Chapter 37 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 37 - Suppose you perform Youngs double-slit experiment...Ch. 37 - A plane monochromatic light wave is incident on a...Ch. 37 - A film of' oil on a puddle in a parking lot shows...Ch. 37 - Prob. 37.1CQCh. 37 - Prob. 37.2CQCh. 37 - Explain why two flashlights held close together do...Ch. 37 - A lens with outer radius of curvature R and index...Ch. 37 - Consider a dark fringe in a double-slit...Ch. 37 - Prob. 37.6CQCh. 37 - What is the necessary condition on the path length...Ch. 37 - In a laboratory accident, you spill two liquids...Ch. 37 - A theatrical smoke machine fills the space bet...Ch. 37 - Two slits are separated by 0.320 mm. A beam of...Ch. 37 - Light of wavelength 530 nm illuminates a pair of...Ch. 37 - A laser beam is incident on two slits with a...Ch. 37 - A Youngs interference experiment is performed with...Ch. 37 - Youngs double-slit experiment is performed with...Ch. 37 - Why is the following situation impossible? Two...Ch. 37 - Light of wavelength 620 nm falls on a double slit,...Ch. 37 - In a Youngs double-slit experiment, two parallel...Ch. 37 - pair of narrow, parallel slits separated by 0.250...Ch. 37 - Light with wavelength 442 nm passes through a...Ch. 37 - The two speakers of a boom box are 35.0 cm apart....Ch. 37 - Prob. 37.12PCh. 37 - Two radio antennas separated by d = 300 in as...Ch. 37 - A riverside warehouse has several small doors...Ch. 37 - A student holds a laser that emits light of...Ch. 37 - A student holds a laser that emits light of...Ch. 37 - Radio waves of wavelength 125 m from a galaxy...Ch. 37 - In Figure P36.10 (not to scale), let L = 1.20 m...Ch. 37 - Coherent light rays of wavelength strike a pair...Ch. 37 - Monochromatic light of wavelength is incident on...Ch. 37 - In the double-slit arrangement of Figure P36.13, d...Ch. 37 - Youngs double-slit experiment underlies the...Ch. 37 - Two slits are separated by 0.180 mm. An...Ch. 37 - Prob. 37.24PCh. 37 - In Figure P37.18, let L = 120 cm and d = 0.250 cm....Ch. 37 - Monochromatic coherent light of amplitude E0 and...Ch. 37 - The intensity on the screen at a certain point in...Ch. 37 - Green light ( = 546 nm) illuminates a pair of...Ch. 37 - Two narrow, parallel slits separated by 0.850 mm...Ch. 37 - A soap bubble (n = 1.33) floating in air has the...Ch. 37 - A thin film of oil (n = 1.25) is located on...Ch. 37 - A material having an index of refraction of 1.30...Ch. 37 - Prob. 37.33PCh. 37 - A film of MgF2 (n = 1.38) having thickness 1.00 ...Ch. 37 - A beam of 580-nm light passes through two closely...Ch. 37 - An oil film (n = 1.45) floating on water is...Ch. 37 - An air wedge is formed between two glass plates...Ch. 37 - Astronomers observe the chromosphere of the Sun...Ch. 37 - When a liquid is introduced into the air space...Ch. 37 - A lens made of glass (ng = 1.52) is coated with a...Ch. 37 - Two glass plates 10.0 cm long are in contact at...Ch. 37 - Mirror M1 in Figure 36.13 is moved through a...Ch. 37 - Prob. 37.43PCh. 37 - One leg of a Michelson interferometer contains an...Ch. 37 - Radio transmitter A operating at 60.0 MHz is 10.0...Ch. 37 - A room is 6.0 m long and 3.0 m wide. At the front...Ch. 37 - In an experiment similar to that of Example 36.1,...Ch. 37 - In the What If? section of Example 36.2, it was...Ch. 37 - An investigator finds a fiber at a crime scene...Ch. 37 - Raise your hand and hold it flat. Think of the...Ch. 37 - Two coherent waves, coming from sources at...Ch. 37 - In a Youngs interference experiment, the two slits...Ch. 37 - In a Youngs double-slit experiment using light of...Ch. 37 - Review. A flat piece of glass is held stationary...Ch. 37 - A certain grade of crude oil has an index of...Ch. 37 - The waves from a radio station can reach a home...Ch. 37 - Interference effects are produced at point P on a...Ch. 37 - Measurements are made of the intensity...Ch. 37 - Many cells are transparent anti colorless....Ch. 37 - Consider the double-slit arrangement shown in...Ch. 37 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 37 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 37 - In a Newtons-rings experiment, a plano-convex...Ch. 37 - Why is the following situation impossible? A piece...Ch. 37 - A plano-concave lens having index of refraction...Ch. 37 - A plano-convex lens has index of refraction n. The...Ch. 37 - Interference fringes are produced using Lloyds...Ch. 37 - Prob. 37.68APCh. 37 - Astronomers observe a 60.0-MHz radio source both...Ch. 37 - Figure CQ37.2 shows an unbroken soap film in a...Ch. 37 - Our discussion of the techniques for determining...Ch. 37 - The condition for constructive interference by...Ch. 37 - Both sides of a uniform film that has index of...Ch. 37 - Prob. 37.74CPCh. 37 - Monochromatic light of wavelength 620 nm passes...Ch. 37 - Prob. 37.76CP
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