88. A spaceship heads away from Earth at 0.20c. The ship beams 450-nm light toward Earth. The light strikes a mirror on Earth and is reflected back to the ship. What is the wavelength of light received by the ship? Hint: Find the wavelength received at Earth, and then consider tha the mirror effectively retransmits light of that wavelength.

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**Task:**

- **Problem Statement:** Do 20-88. Give the answer for \( v/c = 0.25 \).

- **Given Value:** 587.26 nm

**Explanation:**

This exercise involves a calculation related to special relativity, indicated by the term \( v/c \), where \( v \) is velocity and \( c \) is the speed of light. The text prompts to solve problem 20-88 under the condition where the velocity to speed of light ratio is 0.25.

**Details of Given Value:**

- **Wavelength:** The numerical value provided is 587.26 nanometers (nm). This could relate to a specific measurement outcome or condition from the problem being addressed, often potentially linked to parameters like wavelength in Doppler effect scenarios or similar contexts in physics.

**Understanding the Context:**

Without full details of problem 20-88, ensure you understand concepts such as relativistic Doppler effect or potentially Lorentz transformations, depending on the nature of the problem. Applying \( v/c = 0.25 \) involves applying formulas or principles where relativistic effects are non-negligible.
Transcribed Image Text:**Task:** - **Problem Statement:** Do 20-88. Give the answer for \( v/c = 0.25 \). - **Given Value:** 587.26 nm **Explanation:** This exercise involves a calculation related to special relativity, indicated by the term \( v/c \), where \( v \) is velocity and \( c \) is the speed of light. The text prompts to solve problem 20-88 under the condition where the velocity to speed of light ratio is 0.25. **Details of Given Value:** - **Wavelength:** The numerical value provided is 587.26 nanometers (nm). This could relate to a specific measurement outcome or condition from the problem being addressed, often potentially linked to parameters like wavelength in Doppler effect scenarios or similar contexts in physics. **Understanding the Context:** Without full details of problem 20-88, ensure you understand concepts such as relativistic Doppler effect or potentially Lorentz transformations, depending on the nature of the problem. Applying \( v/c = 0.25 \) involves applying formulas or principles where relativistic effects are non-negligible.
**Problem 88: Relativistic Doppler Effect**

A spaceship travels away from Earth at 0.20c. The ship transmits a beam of light with a wavelength of 450 nm toward Earth. This light hits a mirror on Earth and is reflected back to the ship. What is the wavelength of light received by the ship? 

**Hint:** 

1. First, calculate the wavelength received on Earth using the relativistic Doppler effect.
2. Then consider that the mirror on Earth retransmits light of that wavelength back to the ship.
Transcribed Image Text:**Problem 88: Relativistic Doppler Effect** A spaceship travels away from Earth at 0.20c. The ship transmits a beam of light with a wavelength of 450 nm toward Earth. This light hits a mirror on Earth and is reflected back to the ship. What is the wavelength of light received by the ship? **Hint:** 1. First, calculate the wavelength received on Earth using the relativistic Doppler effect. 2. Then consider that the mirror on Earth retransmits light of that wavelength back to the ship.
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