Respuesta :
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
[tex]f = \frac{v}{\lambda} = \frac{3*10^8}{721.4 *10^{-9}} =4.1586*10^{14} \ Hz[/tex]
f = 415.86 THz
Part (b) the speed, wavelength, and frequency of helium-neon laser light in water
refractive index of water = 1.33
[tex]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}[/tex]
[tex]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[/tex]
Again;
[tex]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[/tex]
[tex]f = \frac{v}{\lambda} = \frac{2.26*10^8}{542.4 *10^{-9}} =4.1667*10^{14} \ Hz[/tex]
f = 416.67 THz
Part (c) the speed, wavelength, and frequency of helium-neon laser light in glass
Refractive index of glass = 1.5
[tex]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[/tex]
Also;
[tex]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[/tex]
[tex]f = \frac{v}{\lambda} = \frac{2*10^8}{480.9 *10^{-9}} =4.1588*10^{14} \ Hz[/tex]
f = 415.88 THz
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
