Chapter 7, Problem 7.1QE

Interpretation Introduction

Interpretation:

The characteristics of light waves that would be same and also different between two light sources have to be determined. Also, energy of photons and total energy of the light from the two sources has to be compared.

Concept Introduction:

The wave nature of any light can be described by its frequency, wavelength, and amplitude. The wavelength $\left(\text{λ, lambda}\right)$ of the light is defined as the distance between two successive peaks. Its SI unit is meter. The frequency $\left(v\right)$ is defined as the number of waves that can pass through the one point in 1 second. Its SI unit is ${\text{s}}^{-1}$. The amplitude $\left(A\right)$ of the light wave is maximum height of a wave.

The relation between frequency $\left(v\right)$ and wavelength $\left(\text{λ}\right)$ of the light is as follows:

  $v=\frac{c}{\text{λ}}$        (1)

Here, $c$ is the speed of light, and its value is $3.00\times {10}^8\text{ m/s}$.

Explanation of Solution

The colors of the light sources are the results of the wavelength of the light, and since two light sources have exactly same color thus there value of wavelength $\left(\text{λ}\right)$ are also same.

The expression of relation between wavelength $\left(\text{λ}\right)$ and frequency $\left(v\right)$ is as follows:

  $v=\frac{c}{\text{λ}}$        (1)

Since wavelengths of two light are the same and the speed of light is constant thus frequency of both light sources have same frequency.

The brightness of the light is related to the amplitude of the light wave, and since two light sources as different brightness thus the value of amplitude of both light waves is different.

The expression that relates the energy $\left(E\right)$ of a photon and frequency $\left(v\right)$ is as follows:

  $E=hv$        (2)

Here, $h$ is known as Plank’s constant, and its value is $\text{6}\text{.626}\times {\text{10}}^{-\text{34}}\text{ J}\cdot \text{s}$.

Since the frequency of two light sources are the same and $h$ is a constant, thus two photos have same energy.

Since the brightness of one light source is double than another thus the total energy of light source is also doubled.