Question

The wavelength of red helium-neon laser light in air is 632.8 nm.

(a) What is its frequency?
1 Hz
(b) What is its wavelength in glass that has an index of refractionof 1.48?
2 nm
(c) What is its speed in the glass?
3 Mm/s

Answer 1

Concepts and reason

The concepts to solve this problem are frequency and wavelength of light.

First, find the frequency of the light using the expression of frequency. Then, find the wavelength of light in glass using the concept of refractive index. Finally, find the speed of light in glass medium using the property of refractive index.

Fundamentals

The expression of the frequency of light is as follows:

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

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

The expression of the wavelength of light in a medium other than vacuum is as follows:

$\lambda ' = \frac{\lambda }{n}$

Here, $\lambda$ is the wavelength of light in vacuum and n is the refractive index of medium.

The expression of the refractive index is as follows:

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

Here, c is the speed of light in vacuum and v is the speed of light in a medium.

(a)

The expression of the frequency of light is as follows:

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

Substitute $3.0 \times {10^8}{\rm{ m/s}}$ for c and $632.8{\rm{ nm}}$ for $\lambda$ in the above expression.

$\begin{array}{c}\\f = \frac{{3.0 \times {{10}^8}{\rm{ m/s}}}}{{632.8{\rm{ nm}}}}\left( {\frac{{1{\rm{ nm}}}}{{{{10}^{ - 9}}{\rm{ m}}}}} \right)\\\\ = 4.74 \times {10^{14}}{\rm{ Hz}}\\\end{array}$

(b)

The expression of the wavelength of light in a medium other than vacuum is as follows:

$\lambda ' = \frac{\lambda }{n}$

Substitute $632.8{\rm{ nm}}$ for $\lambda$ and 1.48 for n in the above expression.

$\begin{array}{c}\\\lambda ' = \frac{{632.8{\rm{ nm}}}}{{1.48}}\\\\ = 427.57{\rm{ nm}}\\\end{array}$

(c)

The expression of the speed of light in a medium other than the vacuum is as follows:

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

Substitute $3.0 \times {10^8}{\rm{ m/s}}$ for c and 1.48 for n in the above expression.

$\begin{array}{c}\\v = \frac{{3.0 \times {{10}^8}{\rm{ m/s}}}}{{1.48}}\\\\ = \left( {2.03 \times {{10}^8}{\rm{ m/s}}} \right)\left( {\frac{{1{\rm{ Mm/s}}}}{{{{10}^6}{\rm{ m/s}}}}} \right)\\\\ = 203{\rm{ Mm/s}}\\\end{array}$

Ans: Part a

The frequency is $4.74 \times {10^{14}}{\rm{ Hz}}$

Part b

The wavelength of light in glass is 427.6 nm.

Part c

The speed of light in glass is 203 Mm/s.