Question

The red light from a helium-neon laser has a wavelength of 721.4 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

Answer:

(a) the speed of helium-neon laser light in air is 3 x 10⁸ m/s

     the wavelength of helium-neon laser light in air is 721.4 nm

     the frequency of helium-neon laser light in air is 415.86 THz

(b)  the speed of helium-neon laser light in water is 2.26 x 10⁸ m/s

     the wavelength of helium-neon laser light in water is  542.4nm

     the frequency of helium-neon laser light in water is    416.67THz

(c) the speed of helium-neon laser light in glass is 2 x 10⁸ m/s

    the wavelength of helium-neon laser light in glass is  480.9nm

    the frequency of helium-neon laser light in glass is  415.88THz

From the results above, it can be seen that speed of the light is directly proportional to its wavelength, while the frequency of the light remained fairly constant for the different media.

Explanation:

Part (a) the speed, wavelength, and frequency of helium-neon laser light in air

Given;

wavelength of helium-neon laser light in air, λ = 721.4 nm

speed of light in air, v = 3 x 10⁸ m/s

v = f λ

where;

f is the frequency of helium-neon laser light in air

$f = \frac{v}{\lambda} = \frac{3*10^8}{721.4 *10^{-9}} =4.1586*10^{14} \ Hz$

f = 415.86 THz

Part (b) the speed, wavelength, and frequency of helium-neon laser light in water

refractive index of water = 1.33

$Refractive \ index \ of \ water =\frac{speed \ of \ light \ in \ air}{speed \ of \ light \ in \ water} = \frac{wavelength \ of \ light \ in \ air}{wavelength \ of \ light \ in \ water}$

$speed \ of \ light \ in \ water = \frac{speed \ of \ light \ in \ air}{Refractive \ index \ of \ water} \\\\speed \ of \ light \ in \ water = \frac{3*10^8}{1.33} = 2.26 *10^8 \ m/s$

Again;

$wavelength \ of \ light \ in \ water = \frac{wavelength \ of \ light \ in \ air}{Refractive \ index \ of \ water} \\\\wavelength \ of \ light \ in \ water = \frac{721.4 \ nm}{1.33} = 542.4 \ nm$

$f = \frac{v}{\lambda} = \frac{2.26*10^8}{542.4 *10^{-9}} =4.1667*10^{14} \ Hz$

f = 416.67 THz

Part (c) the speed, wavelength, and frequency of helium-neon laser light in glass

Refractive index of glass = 1.5

$speed \ of \ light \ in \ glass = \frac{speed \ of \ light \ in \ air}{Refractive \ index \ of \ glass} \\\\speed \ of \ light \ in \ glass = \frac{3*10^8}{1.5} = 2 *10^8 \ m/s$

Also;

$wavelength \ of \ light \ in \ glass = \frac{wavelength \ of \ light \ in \ air}{Refractive \ index \ of \ glass} \\\\wavelength \ of \ light \ in \ glass = \frac{721.4 \ nm }{1.5} = 480.9 \ nm$

$f = \frac{v}{\lambda} = \frac{2*10^8}{480.9 *10^{-9}} =4.1588*10^{14} \ Hz$

f = 415.88 THz

Answer 2

Answer:

1) In Air

Speed =  3 * 10⁸m/s

Wavelength = 667.5 nm

Frequency = 4.49 * 10¹⁴Hz

2) In water

Speed =  2.26 * 10⁸m/s

Wavelength = 501.87 nm

Frequency = 4.5 * 10¹⁴Hz

2) In glass

Speed =  2.0 * 10⁸m/s

Wavelength = 445 nm

Frequency = 4.5 * 10¹⁴Hz

Explanation:

1) In AIR

The refractive index for air, n=1

a) The speed of air, c = 3 * 10⁸m/s²

Speed, v = c/n

Since n =1, v = c =  3 * 10⁸m/s

b) wavelength

λ₀ = 667.5 nm

λ = λ₀/n

λ = λ₀ =  667.5 nm

c) Frequency

v = λf

f = v/λ

f = 3 * 10⁸/ 667.5 * 10⁻⁹

f = 4.49 * 10¹⁴Hz

2) In Water

The refractive index of water, n = 1.33

a) Speed, v = c/n

Speed, v = 3 * 10⁸/1.33

v =  2.26 * 10⁸ m/s

b) Wavelength

λ₀ = 667.5 nm

λ = λ₀/n

λ = 667.5 * 10⁻⁹/1.33

λ = 501.87 nm

c) Frequency

f = v/λ

f = 2.26 * 10⁸ /501.87 * 10⁹

f = 4.5 * 10¹⁴Hz

3) In glass

The refractive index of water, n = 1.5

a) Speed, v = c/n

Speed, v = 3 * 10⁸/1.5

v =  2.0 * 10⁸ m/s

b) Wavelength

λ₀ = 667.5 nm

λ = λ₀/n

λ = 667.5 * 10⁻⁹/1.5

λ = 445 nm

c) Frequency

f = v/λ

f = 2.0 * 10⁸ /445* 10⁹

f = 4.5 * 10¹⁴Hz