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The attatched figure shows a Michelson interferometer with a movable mirror M1, a fixed mirror M2, and a beam splitter Ms , which is a half-silvered mirror that transmits one-half the light and reflects one-half the light incident upon it independent of the direction of the light. The source emits monochromatic light of wavelength λ.  Assume the beam splitter introduces a phase change of π for light that follows path 1 from the source to the detector relative to light that follows path 2 from the source to the detector. Also assume the mirrors M1 and M2 reflect 100% ofthe light incident upon them and the photodetector PM (a photomultiplier) is 100% efficient as well. Question:  Use the principles of quantum mechanics to determine the probability that a photon entering the interferometer is detected by the photodetector. Express your answer in terms of the lengths I1 , I2 and λ. Find an expression for I1 in terms of I2 and λ, such that there is 100% probability that the photon is detected by the photodetector.

The attatched figure shows a Michelson interferometer with a movable mirror M1, a fixed mirror M2, and a beam splitter Ms , which is a half-silvered mirror that transmits one-half the light and reflects one-half the light incident upon it independent of the direction of the light. The source emits monochromatic light of wavelength λ.  Assume the beam splitter introduces a phase change of π for light that follows path 1 from the source to the detector relative to light that follows path 2 from the source to the detector. Also assume the mirrors M1 and M2 reflect 100% ofthe light incident upon them and the photodetector PM (a photomultiplier) is 100% efficient as well. Question:  Use the principles of quantum mechanics to determine the probability that a photon entering the interferometer is detected by the photodetector. Express your answer in terms of the lengths I1 , I2 and λ. Find an expression for I1 in terms of I2 and λ, such that there is 100% probability that the photon is detected by the photodetector.

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The attatched figure shows a Michelson interferometer with a movable mirror M1, a fixed mirror M2, and a beam splitter Ms , which is a half-silvered mirror that transmits one-half the light and reflects one-half the light incident upon it independent of the direction of the light. The source emits monochromatic light of wavelength λ. 

Assume the beam splitter introduces a phase change of π for light that follows path 1 from the source to the detector relative to light that follows path 2 from the source to the detector. Also assume the mirrors M1 and M2 reflect 100% ofthe light incident upon them and the photodetector PM (a photomultiplier) is 100% efficient as well.

Question:

  •  Use the principles of quantum mechanics to determine the probability that a photon entering the interferometer is detected by the photodetector. Express your answer in terms of the lengths I1 , I2 and λ. Find an expression for I1 in terms of I2 and λ, such that there is 100% probability that the photon is detected by the photodetector.
**Figure 1.43 The Michelson Interferometer** The diagram illustrates a Michelson interferometer, a device that uses the interference of light waves to make precise measurements. It consists of the following components: - **Source**: The origin point of light in the interferometer. - **M₁ (Movable Mirror)**: A mirror that can be adjusted to change the length of the light path (Path 1). - **M₂ (Fixed Mirror)**: A mirror that remains stationary, providing a constant light path (Path 2). - **M₅ (Half-silvered Mirror)**: This mirror is positioned at a 45-degree angle. It partially reflects and partially transmits incoming light, splitting it into two paths. - **Path 1**: The light travels from the half-silvered mirror to the movable mirror (M₁), with a path length of l₁. - **Path 2**: The light travels from the half-silvered mirror to the fixed mirror (M₂), with a path length of l₂. **Functionality**: The light from the source hits the half-silvered mirror and is split along two paths. One beam travels to the movable mirror (Path 1) and the other to the fixed mirror (Path 2). After reflecting off the mirrors, both beams recombine at the half-silvered mirror. The path difference between Path 1 and Path 2 causes interference, which can be observed and measured. By analyzing the interference pattern, precise measurements can be derived, such as changes in distance or the wavelength of light.
Transcribed Image Text:**Figure 1.43 The Michelson Interferometer** The diagram illustrates a Michelson interferometer, a device that uses the interference of light waves to make precise measurements. It consists of the following components: - **Source**: The origin point of light in the interferometer. - **M₁ (Movable Mirror)**: A mirror that can be adjusted to change the length of the light path (Path 1). - **M₂ (Fixed Mirror)**: A mirror that remains stationary, providing a constant light path (Path 2). - **M₅ (Half-silvered Mirror)**: This mirror is positioned at a 45-degree angle. It partially reflects and partially transmits incoming light, splitting it into two paths. - **Path 1**: The light travels from the half-silvered mirror to the movable mirror (M₁), with a path length of l₁. - **Path 2**: The light travels from the half-silvered mirror to the fixed mirror (M₂), with a path length of l₂. **Functionality**: The light from the source hits the half-silvered mirror and is split along two paths. One beam travels to the movable mirror (Path 1) and the other to the fixed mirror (Path 2). After reflecting off the mirrors, both beams recombine at the half-silvered mirror. The path difference between Path 1 and Path 2 causes interference, which can be observed and measured. By analyzing the interference pattern, precise measurements can be derived, such as changes in distance or the wavelength of light.
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