Chapter U5.114, Problem 3E

Interpretation Introduction

(a)

Interpretation:

The sketches of two waves need to be drawn to show the difference between green light and blue light. The appropriate wavelengths of these two waves need to be determined.

Concept introduction:

The wavelength of a wave is defined as the distance between two consecutive crest and trough.

Explanation of Solution

The waves for short and long wavelength are represented as follows:

From the visible spectra, the range of wavelength for green and blue light is 560-520 nm and 490-450 nm respectively.

Thus, blue light has short wavelength than green light. The sketches of two waves will be as follows:

Interpretation Introduction

(b)

Interpretation:

The approximate frequencies of these two waves need to be determined.

Concept introduction:

The frequency of the wave is defined as number of waves passing a point in 1 second.

Explanation of Solution

The relation between wavelength and frequency is as follows:

$\lambda =\frac{c}{\upsilon }$

Here, $\lambda$ is wavelength, c is speed of light and $\upsilon$ is frequency of the wave.

Since, wavelength is inversely proportional to the frequency thus; green light has low frequency than blue light.

Thus, the wave with short wavelength have high frequency and wave with long wavelength have low frequency.

From the visible region, the range of frequency for green and blue light is 540 to 580 THz and 610-670 THz respectively.

Interpretation Introduction

(c)

Interpretation:

The speed of the travelling waves needs to be determined.

Concept introduction:

The wavelength of light is inversely proportional to frequency.

$\lambda \propto \frac{1}{\upsilon }$

When this proportionality constant is removed, a constant c is used.

$\lambda =\frac{c}{\upsilon }$

This c is speed of light.

Explanation of Solution

The relation between wavelength and frequency is as follows:

$\lambda =\frac{c}{\upsilon }$

Here, $\lambda$ is wavelength, c is speed of light and $\upsilon$ is frequency of the wave.

The speed of light is a constant with value $3\times {10}^8\text{ m/s}$ thus; it is same for both green and blue light.