Question

The wavelength of red helium-neon laser light in air is 632.8 nm.(a) What is its frequency? Hz(b) What is its wavelength in glass that has an index of refractionof 1.48? nm(c) What is its speed in the glass? Mm/s

Answer 1

Answers:

The speed of a wave is given by:

$v=f.\lambda$  (1)

Where $f$ is the frequency and  $\lambda$ the wavelength.

In the case of light, its speed is:

$c=f.\lambda$ (2)

On the other hand, the described situation is known as Refraction,   a phenomenon in which the light changes its direction when passing through a medium with a refractive index different from the other medium.  

In this context, the Refractive index $n$ is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum ($c=3(10)^{8}m/s$) and the speed of light $v$ in the second medium:

$n=\frac{c}{v}$ (3)

In addition, as the light changes its direction, its wavelength changes as well:

$n=\frac{\lambda_{air}}{\lambda_{glass}}$ (4)

Knowing this, let's begin with the answers:

a) Frequency

From equation (2) we can find $f$:

$f=\frac{c}{\lambda}$  (5)

Knowing that $1nm=(10)^{-9}m$:

$f=\frac{3(10)^{8}m/s}{632.8(10)^{-9}m}$  

$f=4.74(10)^{14}Hz}$     (6)   >>>Frequency of the helium-neon laser light

b) Wavelength in glass

We already know the wavelength of the light in air $\lambda_{air}$ and the index of refraction of the glass.

So, we only have to find the wavelength in glass $\lambda_{glass}$ from equation (4):

$\lambda_{glass}=\frac{\lambda_{air}}{n}$

$\lambda_{glass}=\frac{632.8(10)^{-9}m}{1.48}$

$\lambda_{glass}=427(10)^{-9}m=427nm$   (7)   >>>Wavelength of the helium-neon laser light in glass

c) Speed in glass

From equation (3) we can find the speed $v$of this light in glass:

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

$v=\frac{3(10)^{8}m/s}{1.48}$

$v=2.027(10)^{8}m/s$   (8)  >>>Speed of the helium-neon laser light in glass