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Question
How does the speed of light determine the optical density of a medium?
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Solution 1
If the speed of light in a medium is less than the speed of light in air, means the MEDIUM is DENSER than air.
If the speed of light is more than the speed of light in AIR, means the MEDIUM is LESS DENSER than air.
Speed of light is 1/density of medium
Solution 2
- Definition of Optical Density: Optical density refers to how much a medium can slow down the speed of light compared to its speed in a vacuum.
- Speed of Light in Different Media: Light travels fastest in a vacuum (c = 3 × 108 m/s). When light enters a medium (like water, glass, or air), its speed decreases depending on the medium's optical density.
- Relation Between Speed and Optical Density: The greater the optical density, the slower the speed of light in the medium. For example, light travels more slowly in glass than in air because glass has a higher optical density.
- Refractive Index: The optical density is quantified using the refractive index (n), which is defined as: `n = c/v`
- Example:
- In air: n ≈ 1, light speed is almost the same as in a vacuum.
- In water: n ≈ 1.33, light slows down significantly.
- In glass: n ≈ 1.5, light slows down even more.
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