Apply relative refractive index
Scenario
Pehle humne light ko hawa (air) se glass mein bheja. Par agar light pehle se hi paani mein ho aur wahan se glass mein jaaye, tab kitna mudegi?
Do alag-alag materials (air ke bina) ke beech light ki bending ko kaise compare karte hain?
Mental model
Relative index = Destination ki speed-braking power / Source ki speed-braking power.
Jab light medium `1` se medium `2` mein jati hai, toh hum Relative Refractive Index (`n21`) nikalte hain. `n21` ka matlab hai ki pehle wale medium ke comparison mein doosra medium kitna ghana hai. Iska formula speed aur absolute index dono se banta hai.
Explanation
Absolute refractive index (`n`) humesha vacuum (ya hawa) ke reference mein hota hai. Par kya hoga agar light water (medium `1`) se glass (medium `2`) mein travel kare?
Aisi situation mein hum 'Relative Refractive Index' nikalte hain, jise hum `n21` (Refractive index of medium `2` with respect to medium `1`) likhte hain. Ise nikalne ke do tareeqe hain:
1. Speeds ke zariye: `n21 = (Speed of light in medium 1) / (Speed of light in medium 2) = v1 / v2`. Dhyan do, medium `1` upar hai aur medium `2` neeche.
2. Absolute refractive index ke zariye: `n21 = n2 / n1`. Yahan medium `2` ka apna absolute index upar hota hai aur medium `1` ka neeche. Yeh bohot commonly use hota hai.
Agar aap `n12` nikalna chaho (Refractive index of medium `1` with respect to medium `2`), toh woh `n21` ka exactly ulta (reciprocal) hota hai. Yani `n12 = 1 / n21`. Yeh formula MCQs solve karne ke liye trick jaisa kaam karta hai.
Worked example
Problem: Light travels from water (medium `1`, `v1 = 2.25 × 10^8 m/s`) to glass (medium `2`, `v2 = 2 × 10^8 m/s`). What is the refractive index of glass with respect to water (`n21`)?
- Relative index aur speed ka formula use karein.
- Speeds ki values daalein.
- Fraction ko simplify karein.
Answer: `n21 = 1.125`
Problem: Refractive index of glass is `1.5` (`n_g`) and water is `1.33` (`n_w`). What is the refractive index of glass with respect to water?
- Relative index ko absolute indices se jodne wala formula lagayein.
- Values ko formula mein daalein.
Answer: `n_gw = 1.128` (approx)
Key points
- Speed Formula: `n21 = v1 / v2`. (Speed in medium `1` over speed in medium `2`)
- Index Formula: `n21 = n2 / n1`. (Absolute index of medium `2` over absolute index of medium `1`)
- Reciprocal Relation: `n12 = 1 / n21`.
Common mistakes
- Flipping the numerator and denominator: Sabse badi galti yeh hoti hai ki bacche `n21` mein `v2 / v1` kar dete hain. Yaad rakho: `n21` mein absolute `n` ka ratio `n2 / n1` hota hai, par velocities mein ye ulta hota hai: `v1 / v2`.
Recall questions
- What is the formula for refractive index of medium 2 with respect to medium 1 (`n21`) in terms of speeds `v1` and `v2`?
- What is the relation between `n12` and `n21`?
- What does `n21` represent?
Questions & answers
The refractive index of water with respect to air is `4/3` and that of glass with respect to air is `3/2`. Find the refractive index of glass with respect to water.
`9/8`
Approach: `n_gw = n_g / n_w = (3/2) / (4/3) = 9/8`.
If `n21 = 1.5`, what is the value of `n12`?
`n12 = 1 / 1.5 = 0.67`
Approach: Use the property that `n12` is the reciprocal of `n21`.