Determine the speed, wavelength, and frequency of light from a helium-neon laser as it travels through diamond. The wavelength of the light from the laser is 632.8 nm in air and the index of refraction of diamond is 2.419.

speed =  1.24 ×  10⁸m/s

frequency = 4.74 × 10¹⁴Hz

wavelength = 262nm

Explanation:

the speed of the helium-neon light in zircon is given by,

v = c / n

c = 3 × 10⁸m/s is the speed of light in vacuum (and in air)

n = 2.419 is the refractive index of diamond

v = 3 × 10⁸ / 2.419

= 1.24 ×  10⁸m/s

(b) Frequency

The wavelength of the light in air is:

λ₀ = 632.8 × 10⁻⁹

The frequency of the light does not depend on the medium, so it is equal in air and in diamond. Therefore, we can calculate the frequency by using the speed of light in air and the wavelength in air:

f₀ = c / λ₀

= 3 × 10⁸ / 632.8 × 10⁻⁹

= 4.74 × 10¹⁴Hz

and the frequency of the light indiamond is the same:

f¹ = f₀ =  4.74 × 10¹⁴Hz

(c) Wavelength

To calculate the wavelength of the light in daimond, we can use the relationship between speed of light in diamond and frequency:

λ¹ = v / f¹

= 1.24 ×  10⁸ / 4.74 × 10¹⁴

= 2.62 × 10⁻⁷m

= 262nm

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