Answer :
When light travels through different media, its speed is lower than the commonly known value of [tex]\( 3.0 \times 10^8 \)[/tex] meters per second (m/s), which is the speed of light in a vacuum. Here is a detailed explanation of why this happens:
### Interactions with Particles
As light moves through a medium, it interacts with the particles (atoms or molecules) within that medium. These interactions involve processes of absorption and re-emission of the light photons by the particles.
1. Absorption and Re-emission:
- When a photon of light enters a medium, it may be absorbed by an atom or molecule. This excites the particle to a higher energy state.
- Almost immediately, the excited particle will return to its original state by re-emitting a photon. This re-emitted photon continues to travel through the medium until it encounters another particle.
- This cycle of absorption and re-emission introduces slight delays to the overall travel time of the light photon as it traverses the medium.
2. Reduction in Effective Speed:
- Although the individual interactions are extremely brief, the cumulative effect of many such interactions is significant. It effectively reduces the speed at which the light travels through the medium.
- The denser the medium (i.e., the more particles per unit volume), the more frequent the interactions, and thus the slower the resultant speed of light.
### Refractive Index
The phenomenon of light slowing down in a medium is quantified by the medium's refractive index ([tex]\( n \)[/tex]).
- Definition:
The refractive index of a medium is defined as the ratio of the speed of light in a vacuum ([tex]\( c \)[/tex]) to the speed of light in that medium ([tex]\( v \)[/tex]):
[tex]\[ n = \frac{c}{v} \][/tex]
where [tex]\( c \approx 3.0 \times 10^8 \)[/tex] m/s is the speed of light in a vacuum and [tex]\( v \)[/tex] is the speed of light in the medium.
- Impact on Speed:
Since [tex]\( n \)[/tex] is always greater than 1 for any medium other than a vacuum, it follows that [tex]\( v \)[/tex] (the speed of light in the medium) is always less than [tex]\( c \)[/tex]:
[tex]\[ v = \frac{c}{n} \][/tex]
### Example: Light in Water
For example, consider light passing through water, which has a refractive index of approximately 1.33:
[tex]\[ v_{\text{water}} = \frac{c}{n_{\text{water}}} \approx \frac{3.0 \times 10^8}{1.33} \approx 2.26 \times 10^8 \text{ m/s} \][/tex]
Thus, the speed of light in water is approximately [tex]\( 2.26 \times 10^8 \)[/tex] m/s, which is lower than in a vacuum.
### Summary
The speed of light is lower than [tex]\( 3.0 \times 10^8 \)[/tex] m/s in different media due to the interactions between light photons and the particles within the medium. These interactions slow down the effective speed of light as it travels, and this effect is described quantitatively by the medium's refractive index.
### Conclusion
The reduction in the speed of light as it traverses various media (such as air, water, or glass) is a consequence of the physical interactions between light and the particles in the medium, effectively increasing the time it takes for the light to pass through.
### Interactions with Particles
As light moves through a medium, it interacts with the particles (atoms or molecules) within that medium. These interactions involve processes of absorption and re-emission of the light photons by the particles.
1. Absorption and Re-emission:
- When a photon of light enters a medium, it may be absorbed by an atom or molecule. This excites the particle to a higher energy state.
- Almost immediately, the excited particle will return to its original state by re-emitting a photon. This re-emitted photon continues to travel through the medium until it encounters another particle.
- This cycle of absorption and re-emission introduces slight delays to the overall travel time of the light photon as it traverses the medium.
2. Reduction in Effective Speed:
- Although the individual interactions are extremely brief, the cumulative effect of many such interactions is significant. It effectively reduces the speed at which the light travels through the medium.
- The denser the medium (i.e., the more particles per unit volume), the more frequent the interactions, and thus the slower the resultant speed of light.
### Refractive Index
The phenomenon of light slowing down in a medium is quantified by the medium's refractive index ([tex]\( n \)[/tex]).
- Definition:
The refractive index of a medium is defined as the ratio of the speed of light in a vacuum ([tex]\( c \)[/tex]) to the speed of light in that medium ([tex]\( v \)[/tex]):
[tex]\[ n = \frac{c}{v} \][/tex]
where [tex]\( c \approx 3.0 \times 10^8 \)[/tex] m/s is the speed of light in a vacuum and [tex]\( v \)[/tex] is the speed of light in the medium.
- Impact on Speed:
Since [tex]\( n \)[/tex] is always greater than 1 for any medium other than a vacuum, it follows that [tex]\( v \)[/tex] (the speed of light in the medium) is always less than [tex]\( c \)[/tex]:
[tex]\[ v = \frac{c}{n} \][/tex]
### Example: Light in Water
For example, consider light passing through water, which has a refractive index of approximately 1.33:
[tex]\[ v_{\text{water}} = \frac{c}{n_{\text{water}}} \approx \frac{3.0 \times 10^8}{1.33} \approx 2.26 \times 10^8 \text{ m/s} \][/tex]
Thus, the speed of light in water is approximately [tex]\( 2.26 \times 10^8 \)[/tex] m/s, which is lower than in a vacuum.
### Summary
The speed of light is lower than [tex]\( 3.0 \times 10^8 \)[/tex] m/s in different media due to the interactions between light photons and the particles within the medium. These interactions slow down the effective speed of light as it travels, and this effect is described quantitatively by the medium's refractive index.
### Conclusion
The reduction in the speed of light as it traverses various media (such as air, water, or glass) is a consequence of the physical interactions between light and the particles in the medium, effectively increasing the time it takes for the light to pass through.
