A helium-neon laser produces light of wavelength λvac=632.8 nm in vacuum. If this light passes i

A helium-neon laser produces light of wavelength λvac=632.8...

A helium-neon laser produces light of wavelength $\lambda_{\mathrm{vac}}=632.8 \mathrm{nm}$ in vacuum. If this light passes into water, with index of refraction $n=1.333,$ what then will be its
a) speed?
c) wavelength?
b) frequency?
d) color?

Key Concepts

Index of Refraction

The index of refraction is a dimensionless number that describes how much light slows down in a medium compared to its speed in a vacuum. It directly affects other properties such as the speed and wavelength of the light within the medium.

Speed of Light in a Medium

The speed of light in any medium is given by the formula v = c/n, where c is the speed of light in a vacuum and n is the index of refraction. This concept explains why light travels slower in water or glass than in vacuum.

Frequency Invariance

Frequency of a light wave remains constant when transitioning between different media. Since the frequency is determined by the source, it is independent of the medium, ensuring that energy per photon is conserved.

Wavelength Adjustment in a Medium

In a medium, the wavelength of light decreases in proportion to the index of refraction, following the relationship ?_medium = ?_vacuum/n. This reduction in wavelength occurs while the frequency remains unchanged, thereby explaining the changes in spatial periodicity of the light wave.

Color Perception Based on Frequency

The color of light as perceived by the human eye is determined by its frequency (or equivalently its energy), not by its wavelength. Since the frequency remains constant when light enters a different medium, the perceived color remains the same even though the wavelength and speed change.

Transcript

00:01 So in this question we have given helium neon laser of wavelength lambda it is equals to 632 .8 nanometer in the vacuum.

00:09 So it can be represented as lambda vacuum.

00:13 Okay? lambda vacuum.

00:18 So now if light passes into water with refractive index, so n for the water it is equals to 1 .333, then we have to determine the first part speed.

00:30 Okay.

00:30 So speed.

00:32 So speed v, it is equals to c by refractive index n.

00:35 So c is the speed of light into vacuum that is 3 into 10 to the power 8 meter per second divided by 1 .333.

00:42 So from here after solving, speed v.

00:44 Comes out to be 2 .5 multiplied by 10 to the power 8 meter per second.

00:50 Okay? or it can be accurately taken as by taking this value as 2 .998 multiplied by 10 to the power 8 so this value will be nearly exactly equals to 2 .249 multiplied by 10 to the power 8 meter per second so this become the answer for this problem okay now solving for the part b in which we have to determine the wavelength lambda in the medium so in the way medium the wavelength lambda it is equals to it is equal to sorry this is part c so first of all calculating the for the part b and part b is calculating the free so we know that the frequency remains unchanged in the medium.

01:33 So frequency will be equal to a frequency, this will be equals to c by lambda vacuum.

01:40 So c it is equal to 2 .998 multiplied by 10 to the power 8 meter per second and lambda vacuum, it is 632 .8 nanometer that is 10 to the power minus 9 meter.

01:52 So from here after solving frequency f comes out to be 4 .738 multiplied by 10 to the power, 14 hertz.

02:01 So this become the answer for the part b of the problem...

Please give Ace some feedback