Chapter 12: Problem 4

Light travels in water at a speed of $2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}$. Is it possible for particles to travel through water at a speed $v>2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ? Why or why not? Explain.

Short Answer

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Explain your reasoning.

Step by step solution

Speed of light in a vacuum

The speed of light in a vacuum, denoted as $c$, is a universal constant, and its value is approximately $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$.

Speed of light in water

We are given the speed of light in water, which is $2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}$.

Refractive index

The refractive index is the ratio of the speed of light in a vacuum to the speed of light in a material. The refractive index of water, denoted as $n$, can be calculated as follows: $$ n = \frac{c}{v_\text{water}} $$ Where $v_\text{water}$ is the speed of light in water.

Calculate the refractive index of water

Now, let's calculate the refractive index of water using the given values of the speed of light in a vacuum and in water: $$ n = \frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}} = 1.33 $$ So, the refractive index of water is $1.33$.

Determine the maximum possible speed of particles in water

A particle can travel through water at a speed greater than the speed of light in water, but it cannot surpass the speed of light in vacuum, which is $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$. This is due to the laws of physics, which state that nothing can travel faster than the speed of light in vacuum.

Conclusion

It is possible for particles to travel through water at a speed greater than the given $2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}$, but they cannot surpass the maximum speed of $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$, which is the speed of light in a vacuum.

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Light travels in water at a speed of \(2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Is it possible for particles to travel through water at a speed \(v>2.25 \times 10^{8} \mathrm{~m} / \mathrm{s}\) ? Why or why not? Explain.

Short Answer

Step by step solution

Speed of light in a vacuum

Speed of light in water

Refractive index

Calculate the refractive index of water

Determine the maximum possible speed of particles in water

Conclusion

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