Chapter 27, Problem 66A

A light wave has wavelength $\lambda$.

a. Write an equation for the frequency of this light.

b. Convert the following wavelengths to frequencies in Hz: 400 nm, 500 nm, 600 nm, and 700 nm.

c. What happens to the frequency of the light as the wavelength increases?

To determine

The equation for the frequency of light.

Explanation of Solution

Introduction:

The wavelength of the light is $\lambda$ .

In a unit time, the number of waves which are passing through the fixed point is known as the frequency of the light wave.

The frequency of the wave is related to the wavelength and velocity of the light such as

  $f=\frac{c}{\lambda }$

Where $f$ = is the frequency of the light

  $c$ = is the velocity of light

  $\lambda$ = wavelength of the light

Conclusion:

The equation for the frequency of lightis: $f=\frac{c}{\lambda }$

To determine

To Convert:The given wavelengths into frequency.

Explanation of Solution

Given:

The given wavelengths are 400nm, 500nm, 600nm, and 700nm.

Formula Used:

The frequency can be calculated using the formula:

  $f=\frac{c}{\lambda }$

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

Calculations:

Case 1:

For the wavelength: 400 nm

  $\begin{array}{l}f=\frac{c}{\lambda }\\ =\frac{3\times {10}^8}{400\times {10}^{-9}}\\ f=7.5\times {10}^{14}\text{Hz}\end{array}$

Case 2:

For the wavelength: 500nm

  $\begin{array}{l}f=\frac{c}{\lambda }\\ =\frac{3\times {10}^8}{500\times {10}^{-9}}\\ f=6.0\times {10}^{14}\text{Hz}\end{array}$

Case 3: For the wavelength: 600nm

  $\begin{array}{l}f=\frac{c}{\lambda }\\ =\frac{3\times {10}^8}{600\times {10}^{-9}}\\ f=5.0\times {10}^{14}\text{Hz}\end{array}$

Case 4: For the wavelength: 700nm

  $\begin{array}{l}f=\frac{c}{\lambda }\\ =\frac{3\times {10}^8}{700\times {10}^{-9}}\\ f=4.3\times {10}^{14}\text{Hz}\end{array}$

To determine

The effect on the frequency of the light when the wavelength is increased.

Explanation of Solution

Introduction:

The frequency of light:

  $f=\frac{c}{\lambda }$

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

The frequency of the light is inversely dependent on its wavelength. If the wavelength is increased then the frequency is decreased.

Conclusion:

The frequency is decreased.