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Chapter 11: Problem 36

Reflection and Refraction Light of wavelength \(0.500 \mu \mathrm{m}\) (in air) enters the water in a swimming pool. The speed of light in water is 0.750 times the speed in air. What is the wavelength of the light in water?

Short Answer

Expert verified
Answer: The wavelength of light in water is \(0.375 \mu \mathrm{m}\).

Step by step solution

01

Identify the given information

In this problem, we are provided with: 1. Wavelength of light in air: \(0.500 \mu \mathrm{m}\) 2. Ratio of the speed of light in water to the speed of light in air: \(0.750\)
02

Recall the wave equation and the constant frequency rule

The wave equation describes the relationship between the speed of light (v), its frequency (f), and wavelength (λ): $$v = f * λ$$ When light travels from one medium to another (from air to water in this case), its frequency remains constant.
03

Calculate the wavelength of light in water

Since the frequency of light remains constant when it enters a medium, we can simply use the given ratio of the speed of light in water to air: $$\frac{v_{water}}{v_{air}} = 0.750$$ Since the frequency is constant, we can write: $$\frac{f * λ_{water}}{f * λ_{air}} = 0.750$$ The frequencies cancel out, and we are left with: $$\frac{λ_{water}}{λ_{air}} = 0.750$$ Now, we can solve for the wavelength of light in water: $$λ_{water} = λ_{air} * 0.750$$ $$λ_{water} = 0.500\mu \mathrm{m} * 0.750$$ $$λ_{water} = 0.375\mu \mathrm{m}$$
04

Write the final answer

The wavelength of light in water is \(0.375 \mu \mathrm{m}\).

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Most popular questions from this chapter

A transverse wave on a string is described by the equation $y(x, t)=(2.20 \mathrm{cm}) \sin [(130 \mathrm{rad} / \mathrm{s}) t+(15 \mathrm{rad} / \mathrm{m}) x].$ (a) What is the maximum transverse speed of a point on the string? (b) What is the maximum transverse acceleration of a point on the string? (c) How fast does the wave move along the string? (d) Why is your answer to (c) different from the answer to (a)?
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Light visible to humans consists of electromagnetic waves with wavelengths (in air) in the range \(400-700 \mathrm{nm}\) $\left(4.0 \times 10^{-7} \mathrm{m} \text { to } 7.0 \times 10^{-7} \mathrm{m}\right) .$ The speed of light in air is \(3.0 \times 10^{8} \mathrm{m} / \mathrm{s} .\) What are the frequencies of electromagnetic waves that are visible?
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