Explanation Given info: The amplitude of the light in Slit 1 is three times the amplitude of the light in slit 2 . The total magnitude at a point P is superposition of the two waves from two slits. The electric field of two waves is shown as, Figure (1) The resultant electric field at point P is, E R = E 1 + E 2 (1) Here, E 1 is the electric field due to the slit 1 . E 2 is the electric field due to the slit 2 . The electric field due to slit 1 is, E 1 = 3 E 0 sin ω t Here, 3 E 0 is the amplitude of wave 1 from slit 1 . ω is the angular frequency of wave 1 . The electric field due to slit 2 is, E 2 = E 0 sin ( ω t + ϕ ) Here, E 0 is the amplitude of wave 2 from slit 2 . ω is the angular frequency of wave 2 . ϕ is the phase difference of wave 2 . Substitute 3 E 0 sin ω t for E 1 and E 0 sin ( ω t + ϕ ) for E 2 in equation (1). E R = 3 E 0 sin ω t + E 0 sin ( ω t + ϕ ) The magnitude of resultant of two vectors according to cosine law is, E R 2 = ( 3 E 0 ) 2 + ( E 0 ) 2 + 2 ( 3 E 0 ) ( E 0 ) cos ϕ = 9 E 0 2 + E 0 2

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN: 9781305116399

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Diffraction of light

In physics, the term diffraction is defined as the bending of light around the corners of the obstacle. As a light ray passes by an aperture, it bends around the edges or through slits, it spreads out through a narrow opening. The diffracted light will p…

Videos

Question

Chapter 37, Problem 37.74CP

To determine

To show: The expression for the intensity is given by I=Imax(1+3cos2ϕ/2)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 37, Problem 37.73CP

Chapter 37, Problem 37.75CP

Students have asked these similar questions

Please solve this question

Please solve

Questions 68-70 Four hundred millilitres (mL) of a strong brine solution at room temperature was poured into a measuring cylinder (Figure 1). A piece of ice of mass 100 g was then gently placed in the brine solution and allowed to float freely (Figure 2). Changes in the surface level of the liquid in the cylinder were then observed until all the ice had melted. Assume that the densities of water, ice and the brine solution are 1000 kg m-3, 900 kg m3 and 1100 kg m3, respectively. 68 Figure 1 400 400 Figure 2 1m² = 1x10 mL After the ice was placed in the brine solution and before any of it had melted, the level of the brine solution was closest to 485 mL. B 490 mL. C 495 mL. Displaced volume by ice. D 500 mL. weight of ice 69 The level of the brine solution after all the ice had melted was A 490 mL B 495 mL D 1100kg/m² = 909 xious mis 70 Suppose water of the same volume and temperature had been used instead of the brine solution. In this case, by the time all the ice had melted, the…

Chapter 37 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 37 - Which of the following causes the fringes in a...Ch. 37 - Using Figure 36.6 as a model, sketch the...Ch. 37 - One microscope slide is placed on top of another...Ch. 37 - While using a Michelson interferometer (shown in...Ch. 37 - Four trials of Young's double-slit experiment are...Ch. 37 - Suppose Youngs double-slit experiment is performed...Ch. 37 - Green light has a wavelength of 500 nm in air. (i)...Ch. 37 - A thin layer of oil (n = 1.25) is floating on...Ch. 37 - A monochromatic beam of light of wavelength .500...Ch. 37 - According to Table 35.1, the index of refraction...

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. 37.1CQ Ch. 37 - Prob. 37.2CQ Ch. 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. 37.6CQ Ch. 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. 37.12P Ch. 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. 37.24P Ch. 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. 37.33P Ch. 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. 37.43P Ch. 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. 37.68AP Ch. 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. 37.74CP Ch. 37 - Monochromatic light of wavelength 620 nm passes...Ch. 37 - Prob. 37.76CP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The expression for the intensity is given by I = I max ( 1 + 3 cos 2 ϕ / 2 )

Solution Summary: The author explains that the amplitude of the light in a slit is three times the intensity of light. The electric field of two waves is shown as, Figure (1).

Concept explainers

Videos

To show: The expression for the intensity is given by I=Imax(1+3cos2ϕ/2)

Want to see the full answer?

Chapter 37 Solutions