Respuesta :
Answer:
Wavelength = 489.52 nm
Explanation:
Given that the wavelength of the light = 633 nm
The time taken by the light in unknown liquid = 1.38 ns
Also,
1 ns = 10⁻⁹ s
So, t = 1.38 × 10⁻⁹ s
Also,
Distance = 32.0 cm = 0.32 m ( 1 cm = 0.01 m)
So, speed of the light in the liquid = Distance / Time = 0.32 / 1.38 × 10⁻⁹ m/s = 2.32 × 10⁸ m/s
Frequency of the light does not change when light travels from one medium to another. So,
[tex]\frac {V_{air}}{\lambda_{air}}=\frac {V_{liquid}}{\lambda_{liquid}}[/tex]
[tex]{V_{air}}=3\times 10^8\ m/s[/tex]
[tex]{\lambda_{air}}=633\ nm[/tex]
[tex]{V_{liquid}}=2.32\times 10^8\ m/s[/tex]
[tex]{\lambda_{liquid}}=?\ nm[/tex]
So,
[tex]\frac {3\times 10^8\ m/s}{633\ nm}=\frac {2.32\times 10^8\ m/s}{\lambda_{liquid}}[/tex]
Wavelength = 489.52 nm
Wavelength is the distance between two points of the two consecutive waves.
The wavelength of the laser beam in the liquid is 489.52 nm.
What is the wavelength of the wave?
Wavelength is the distance between two points of the two consecutive waves.
Given information-
The helium-neon laser beam has a wavelength in air of 633 nm.
The time taken by the helium laser beam to to travel through 32.0 cm or 0.32 m of an unknown liquid is 1.38 ns or [tex]1.38\times10^{-9}\rm s[/tex].
Speed of the light is the ratio of distance traveled by it in the time taken. Thus the speed of the given light is,
[tex]v=\dfrac{0.32}{1.38}\\v=2.32\times10^8 \rm m/s[/tex]
Frequency of the wave is the ratio of speed and wavelength of the wave.
As the frequency of the wave is equal for each medium. Thus,
[tex]f=\dfrac{v_{liq}}{\lambda_{liq}} =\dfrac{v_{air}}{\lambda_{air}}[/tex]
As the speed of the air is [tex]3\times10^8[/tex] m/s.
Thus put the values in the above ratio as,
[tex]\dfrac{2.32\times10^8}{\lambda_{liq}} =\dfrac{3\times10^8}{633}\\\lambda_{liq}=489.52 \rm nm[/tex]
Thus the wavelength of the laser beam in the liquid is 489.52 nm.
Learn more about the wavelength here;
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