Question 15 of 15 An electromagnetic wave with frequency f = 2 x 1010 Hz is traveling in a transparent material having an index of refraction n = 1.5. What is the wavelength of the wave? 2.0 cm 1.0 cm 2.3 cm 1.5 cm 3.0 cm
Question 15 of 15 An electromagnetic wave with frequency f = 2 x 1010 Hz is traveling in a transparent material having an index of refraction n = 1.5. What is the wavelength of the wave? 2.0 cm 1.0 cm 2.3 cm 1.5 cm 3.0 cm
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question 15 of 15**
An electromagnetic wave with frequency \( f = 2 \times 10^{10} \) Hz is traveling in a transparent material having an index of refraction \( n = 1.5 \). What is the wavelength of the wave?
**Options:**
- 2.0 cm
- 1.0 cm
- 2.3 cm
- 1.5 cm
- 3.0 cm
There are no graphs or diagrams present in this image. This question appears to test understanding of the relationship between wave frequency, speed, and wavelength in a medium with a given index of refraction. To find the wavelength, use the formula:
\[ \lambda = \frac{v}{f} \]
where \( v \) is the speed of light in the given medium and \( f \) is the frequency of the wave. Given that the speed of light \( c \) in vacuum is \( 3 \times 10^8 \) m/s, the speed of light in the material will be:
\[ v = \frac{c}{n} = \frac{3 \times 10^8 \text{ m/s}}{1.5} = 2 \times 10^8 \text{ m/s} \]
Substituting the given frequency:
\[ \lambda = \frac{2 \times 10^8 \text{ m/s}}{2 \times 10^{10} \text{ Hz}} = 0.01 \text{ m} = 1 \text{ cm} \]
Therefore, the correct answer is:
- 1.0 cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7bf774f-fe51-4121-93c6-6dec45c8cd41%2F41ee4342-b2a8-4a01-8f55-bf54472dd467%2Fsxzth6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 15 of 15**
An electromagnetic wave with frequency \( f = 2 \times 10^{10} \) Hz is traveling in a transparent material having an index of refraction \( n = 1.5 \). What is the wavelength of the wave?
**Options:**
- 2.0 cm
- 1.0 cm
- 2.3 cm
- 1.5 cm
- 3.0 cm
There are no graphs or diagrams present in this image. This question appears to test understanding of the relationship between wave frequency, speed, and wavelength in a medium with a given index of refraction. To find the wavelength, use the formula:
\[ \lambda = \frac{v}{f} \]
where \( v \) is the speed of light in the given medium and \( f \) is the frequency of the wave. Given that the speed of light \( c \) in vacuum is \( 3 \times 10^8 \) m/s, the speed of light in the material will be:
\[ v = \frac{c}{n} = \frac{3 \times 10^8 \text{ m/s}}{1.5} = 2 \times 10^8 \text{ m/s} \]
Substituting the given frequency:
\[ \lambda = \frac{2 \times 10^8 \text{ m/s}}{2 \times 10^{10} \text{ Hz}} = 0.01 \text{ m} = 1 \text{ cm} \]
Therefore, the correct answer is:
- 1.0 cm
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