Question

The red light from a helium-neon laser has a wavelength of 727.7 nm in air. Find the speed, wavelength, and frequency of helium-neon laser light in air, water, and glass. (The glass has an index of refraction equal to 1.50.)

Answer 1

speed 2.997 10⁸, 2,254 10⁸, 1,999 10⁸ m / s

`\lambda_(n)` 727.7, 547, 485 nm

Step-by-step explanation:

The index of refraction is defined as the relationship between the speed of light in a vacuum and in a material medium

n = c / v

Let's calculate the speed of light in the media

Air

The refractive index is very close to that of the vacuum n = 1,00029

In most experiments they are considered equal

v = c/ n

v = 2,998 10⁸ / 1,00029

v = 2,997 10⁸ m / s

Water

n = 1.33

v = 2.998 10⁸ / 1.33

v = 2,254 10⁸ m / s

Glass

n = 1.50

v = 2,998 10⁸ / 1,50

v = 1,999 10⁸ m / s

Frequency and wavelength are related by the equation

c = λ f

When a beam with a given frequency hits excites the electrons of the material and induces forced oscillations, which has the same frequency of the incident, so the frequency of the beam does not change when passing from one medium to the other.

As speed changes the only way that equality is maintained is that the wavelength changes

`\lambda_(n)` = λ₀ / n

Air

`\lambda_(n)` =727.7 nm

Water

`\lambda_(n)` = 727.7 / 1.33

`\lambda_(n)` = 547.14 nm

Glass

`\lambda_(n)` = 727.7 / 1.50

`\lambda_(n)` = 485.13 nm