Chapter 16, Problem 1SP

(a)

To determine

The frequencies associated with violet and red end of the spectrum.

Answer to Problem 1SP

The frequency associated with violet light is $7.89\times {10}^{14}\text{Hz}$ and the frequency associated with red light is $4.0\times {10}^{14}\text{Hz}$.

Explanation of Solution

Given info:

The wavelength associated with violet light is $380\text{nm}$ and the wavelength associated with red light is $750\text{nm}$

Write an expression to calculate the frequency of the wave.

$f=\frac{c}{\lambda }$ (1)

Here,

$f$ is the frequency

$c$ is the speed of light

$\lambda$ is the wavelength

For violet light:

Substitute $380\text{nm}$ for $\lambda$ and $3.00\times {10}^8\text{m/s}$ for $c$ in equation (1) to find $f$.

$\begin{array}{c}f=\frac{3.00\times {10}^8\text{m/s}}{\left(380\text{nm}\right)\left(\frac{1\text{m}}{{10}^{-9}\text{nm}}\right)}\\ =7.89\times {10}^{14}\text{Hz}\end{array}$

For red light:

Substitute $750\text{nm}$ for $\lambda$ and $3.00\times {10}^8\text{m/s}$ for $c$ in equation (1) to find $f$.

$\begin{array}{c}f=\frac{3.00\times {10}^8\text{m/s}}{\left(750\text{nm}\right)\left(\frac{1\text{m}}{{10}^{-9}\text{nm}}\right)}\\ =4.0\times {10}^{14}\text{Hz}\end{array}$

Thus, the frequency associated with violet light is $7.89\times {10}^{14}\text{Hz}$ and the frequency associated with red light is $4.0\times {10}^{14}\text{Hz}$.

Conclusion:

The frequency associated with violet light is $7.89\times {10}^{14}\text{Hz}$ and the frequency associated with red light is $4.0\times {10}^{14}\text{Hz}$.

(b)

To determine

The approximate speed of light in glass.

Answer to Problem 1SP

The approximate speed of light in glass is $2.00\times {10}^8\text{m/s}$.

Explanation of Solution

Given info:

The refractive index of glass is $1.5$.

Write an expression for speed of light in glass.

$v=\frac{c}{n}$

Here,

$v$ is the speed of light in glass

$c$ is the speed of light in vacuum

$n$ is the refractive index

Substitute $3.00\times {10}^8\text{m/s}$ for $c$ and $1.5$ for $n$ to find $v$.

$\begin{array}{c}v=\frac{3.00\times {10}^8\text{m/s}}{1.5}\\ =2.00\times {10}^8\text{m/s}\end{array}$

Thus, approximate speed of light in glass is $2.00\times {10}^8\text{m/s}$.

Conclusion:

The approximate speed of light in glass is $2.00\times {10}^8\text{m/s}$.

(c)

To determine

The wavelength’s of two ends of visible spectrum in glass.

Answer to Problem 1SP

The wavelength associated with violet light is $150\text{nm}$ and the wavelength associated with red light is $300\text{nm}$.

Explanation of Solution

Write an expression to calculate the wavelength of the wave.

$\lambda =\frac{v}{f}$ (2)

For violet light:

Substitute $7.89\times {10}^{14}\text{Hz}$ for $f$ and $2.00\times {10}^8\text{m/s}$ for $v$ in equation (2) to find $\lambda$.

$\begin{array}{c}f=\frac{2.00\times {10}^8\text{m/s}}{7.89\times {10}^{14}\text{Hz}}\\ =150\text{nm}\end{array}$

For red light:

Substitute $7.89\times {10}^{14}\text{Hz}$ for $f$ and $2.00\times {10}^8\text{m/s}$ for $v$ in equation (2) to find $\lambda$.

$\begin{array}{c}f=\frac{2.00\times {10}^8\text{m/s}}{4.0\times {10}^{14}\text{Hz}}\\ =300\text{nm}\end{array}$

Thus, the wavelength associated with violet light is $150\text{nm}$ and the wavelength associated with red light is $300\text{nm}$.

Conclusion:

The wavelength associated with violet light is $150\text{nm}$ and the wavelength associated with red light is $300\text{nm}$.