Rank in order the following according to their speeds, from fastest (1) to slowest (5): (i) 425-nm-wavelength light through a pane of glass, (ii) 500-nm-wavelength light through air, (iii) 540-nm-wavelength light through water, (iv) 670-nm-wavelength light through a diamond, and (v) 670-nm-wavelength light through a vacuum.
the answer is just the actual speeds, no math needed.
so v, ii, iii, i, iv
The speed depends on the refractive index of the substance n
n=c/v
1. vacuum: c=3•10⁸ m/s
2. air n= 1.000293 =>
v= c/n =3•10⁸ /1.000293 =2.999•10⁸ m/s
3. water n=1.333
=> v= c/n =3•10⁸ /1.333 =2.25•10⁸ m/s
4. glass n=1.5
=> v= c/n =3•10⁸ /1.5 =2•10⁸ m/s
5. diamond n=2.42
=> v= c/n =3•10⁸ /2.42 =1.24•10⁸ m/s
To rank the following according to their speeds, from fastest to slowest:
1. 670-nm-wavelength light through a vacuum: Light travels at its maximum speed in a vacuum, which is approximately 299,792,458 meters per second.
2. 500-nm-wavelength light through air: Light slows down slightly when traveling through air compared to a vacuum, but the difference is negligible at common atmospheric conditions.
3. 425-nm-wavelength light through a pane of glass: Light travels slower in a medium like glass compared to air or vacuum due to the refractive index of glass.
4. 540-nm-wavelength light through water: Water has a higher refractive index compared to glass, causing light to travel even slower in this medium.
5. 670-nm-wavelength light through a diamond: Diamond has a very high refractive index, which significantly slows down the speed of light compared to all the previous mediums.
Therefore, the ranking from fastest to slowest is: (v), (ii), (i), (iii), (iv).
To rank the given scenarios in order of their speeds from fastest (1) to slowest (5), we need to understand how the speed of light is influenced by different mediums.
The speed of light in a vacuum is considered to be the fastest, which is approximately 299,792,458 meters per second (or about 186,282 miles per second).
When light travels through different mediums, it interacts with the particles of that medium, which can slow it down. The speed of light in any medium is always less than the speed of light in a vacuum.
Now, let's consider the given scenarios and rank them accordingly:
(i) 425-nm-wavelength light through a pane of glass:
When light passes through a medium like glass, its speed decreases. The refractive index of glass is greater than 1, which means the speed of light in glass is slower than in a vacuum.
(ii) 500-nm-wavelength light through air:
Air has a refractive index of very close to 1, indicating that the speed of light in air is very similar to its speed in a vacuum. Therefore, the speed of light through air is slightly slower than in a vacuum but still relatively fast.
(iii) 540-nm-wavelength light through water:
Water has a higher refractive index than air, which means the speed of light in water is slower than in air. Thus, the speed of light through water is slower than light through air.
(iv) 670-nm-wavelength light through a diamond:
Diamond has a very high refractive index, indicating that the speed of light in diamond is significantly lower than in a vacuum or other mediums mentioned before.
(v) 670-nm-wavelength light through a vacuum:
As mentioned earlier, the speed of light in a vacuum is the fastest. Therefore, the speed of light through a vacuum is the highest amongst the mentioned scenarios.
Based on the above explanations, we can rank the scenarios from fastest to slowest as follows:
1. 670-nm-wavelength light through a vacuum
2. 500-nm-wavelength light through air
3. 425-nm-wavelength light through a pane of glass
4. 540-nm-wavelength light through water
5. 670-nm-wavelength light through a diamond