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Chapter 32: Problem 14

Answer as true or false with an explanation for the following: The wavelength of He-Ne laser light in water is less than its wavelength in the air. (The refractive index of water is \(1.33 .\)

Short Answer

Expert verified
Explain your answer. Answer: The statement is True. The wavelength of He-Ne laser light in water is less than its wavelength in the air because the refractive index of water (1.33) is greater than that of air (1), causing the wavelength in water to decrease.

Step by step solution

01

Understand the relation between the speed of light, wavelength and refractive index

The relation between the speed of light in a vacuum 𝑣₀, the speed of light in a medium 𝑣, and the refractive index 𝑛 of that medium can be given as follows: \(n = \frac{v_0}{v}\) Also, the relation between speed, frequency (𝑓), and wavelength (𝜆) is given by \(v = f \lambda\). Considering these two equations, we have: \(n = \frac{v_0}{f\lambda}\).
02

Analyze the statement of the problem

We want to know if the wavelength of He-Ne laser light in water is less than its wavelength in the air. For this, let's compare the wavelengths in water and air. Let the wavelength in air be \(\lambda_1\) and the wavelength in water be \(\lambda_2\). Since the frequency remains constant for the same source of light: \(\frac{n_2}{n_1} = \frac{v_{01}}{v_{02}} = \frac{f\lambda_1}{f\lambda_2}\) where \(n_1=1\) (refractive index of air) and \(n_2=1.33\) (refractive index of water).
03

Calculate the ratio of wavelengths

From the equation above, \(\frac{1.33}{1} = \frac{\lambda_1}{\lambda_2}\) \(\implies 1.33\lambda_2 = \lambda_1\)
04

Determine if the statement is true or false

From the equation \(1.33\lambda_2 = \lambda_1\), we can see that the wavelength in air 𝜆₁ is greater than the wavelength in water 𝜆₂, so the statement "The wavelength of He-Ne laser light in water is less than its wavelength in the air" is True. This is because the refractive index of water is more than that of air, which causes the wavelength to decrease in water.

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Most popular questions from this chapter

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