Relate refractive index to speed of light
Scenario
Space mein light sabse tez (`3 lakh km/s`) chalti hai. Par jab wahi light diamond ya pani mein ghusti hai, toh uski speed kam ho jati hai.
Humein kaise pata chalega ki kis material mein light ki speed kitni kam hogi?
Mental model
Refractive index ek 'Speed Breaker' score hai.
Jitna bada refractive index (`n`), utna bada speed breaker. Absolute Refractive Index humein batata hai ki us medium ne light ki speed ko vacuum ke comparison mein kitne guna (times) slow kar diya.
Explanation
Refractive Index (jise hum `n` se likhte hain) sirf angles ke baare mein nahi hai. Iska direct relation speed of light se hota hai. Jab light vacuum (ya air) se kisi aur medium mein enter karti hai, toh medium ke atoms light ko resist karte hain aur uski speed kam kar dete hain.
Absolute Refractive Index ka formula hai: `n = Speed of light in vacuum (c) / Speed of light in medium (v)`.
Vacuum mein light ki speed `c` fix hoti hai: `3 × 10^8 m/s`. (Air mein bhi hum lagbhag yahi value use karte hain).
Agar kisi glass ka refractive index `1.5` hai, iska seedha sa matlab hai ki glass ne light ki speed ko vacuum se `1.5` times kam kar diya hai. Yani `v = c / 1.5`. Diamond ka refractive index sabse zyada (`2.42`) hota hai, iska matlab diamond light ko sabse zyada slow kar deta hai (speed `2.42` times kam ho jati hai).
Kyunki `n = c / v` ek ratio hai do speeds ka, isliye iski koi unit nahi hoti. Yeh sirf ek pure number hota hai. Hamesha `n` ki value `1` se badi hogi, kyunki kisi bhi cheez mein light vacuum se tez nahi chal sakti.
Worked example
Problem: Light enters from air to glass having refractive index `1.50`. What is the speed of light in the glass? (Speed of light in vacuum is `3 × 10^8 m/s`)
- Absolute refractive index ka formula lagayein.
- Equation ko rearrange karein taaki medium ki speed (v) nikal sake.
- Values ko formula mein daalein.
- Calculate the result.
Answer: Speed of light in glass is `2 × 10^8 m/s`
Problem: The speed of light in a transparent liquid is `2.5 × 10^8 m/s`. Find its absolute refractive index.
- Formula n = c / v hota hai.
- 10^8 wali terms cancel ho jayengi.
- Fraction ko simplify karein.
Answer: Refractive index = `1.2`
Key points
- Absolute Refractive Index Formula: `n = c / v` (where `c = 3 × 10^8 m/s`, and `v` is speed in the medium).
- No Units: Refractive index is a ratio of similar quantities (speed/speed), so it has no SI unit.
- Optical Density: Higher refractive index means higher optical density and slower speed of light.
Common mistakes
- Writing unit for Refractive Index: Exam mein bacche jaldi mein answer ke aage `m/s` ya koi aur unit likh dete hain. Refractive index ek dimensionless ratio hai, uska koi unit nahi hota.
Recall questions
- What is the formula connecting refractive index and speed of light?
- What is the unit of refractive index?
- What is the formula relating absolute refractive index and speed of light?
Questions & answers
The refractive index of diamond is `2.42`. What is the meaning of this statement?
It means the ratio of the speed of light in vacuum to the speed of light in diamond is `2.42`. Light travels `2.42` times slower in diamond than in vacuum.
Approach: Define `n = c / v`, and plug in `2.42 = c / v`.
If the speed of light in glass is `2 × 10^8 m/s`, what is its refractive index? (`c = 3 × 10^8 m/s`)
`n = 1.5`
Approach: `n = c / v = (3 × 10^8) / (2 × 10^8) = 1.5`
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