Refractive index of benzene 32 find the speed of light in benzene
The correct answer and explanation is:
Let’s solve the problem step-by-step.
Given:
- Refractive index of benzene, n = 1.32
- Speed of light in vacuum, c = 3.00 × 10^8 m/s
Find:
- Speed of light in benzene, v
Formula:
The refractive index nn is defined as: n=cvn = \frac{c}{v}
where
- cc is the speed of light in vacuum,
- vv is the speed of light in the medium (here, benzene).
Rearranging the formula to find vv: v=cnv = \frac{c}{n}
Calculation:
v=3.00×108 m/s1.32=2.27×108 m/sv = \frac{3.00 \times 10^8 \text{ m/s}}{1.32} = 2.27 \times 10^8 \text{ m/s}
Final answer:
The speed of light in benzene is approximately 2.27 × 10^8 meters per second.
Explanation (300 words):
The refractive index of a medium is a measure of how much the speed of light is reduced inside that medium compared to its speed in a vacuum. It is a dimensionless quantity defined by the ratio of the speed of light in vacuum to the speed of light in the medium: n=cvn = \frac{c}{v}
In this case, the refractive index nn of benzene is given as 1.32, meaning light travels slower in benzene than it does in vacuum by this factor.
The speed of light in vacuum cc is a universal constant, approximately 3.00×1083.00 \times 10^8 meters per second. This value is the fastest speed at which light or any electromagnetic wave can travel.
Since benzene has a refractive index greater than 1, it means light slows down when passing through benzene molecules. This reduction happens because light interacts with the electrons in benzene molecules, causing it to be absorbed and re-emitted, which takes time and effectively slows the light’s progress.
By dividing the speed of light in vacuum by the refractive index, we get the actual speed of light in benzene: v=3.00×108 m/s1.32=2.27×108 m/sv = \frac{3.00 \times 10^8 \, m/s}{1.32} = 2.27 \times 10^8 \, m/s
This calculation shows that light moves approximately 27% slower in benzene than in vacuum.
Understanding refractive indices is important in optics and physics because it helps in designing lenses, prisms, and other optical devices. It also explains phenomena like bending of light (refraction) when it passes from one medium to another, which is the principle behind lenses focusing light.