Apply laws of refraction (Snell's Law)
Scenario
Agar aap laser light ko alag-alag angle se glass mein maarte ho, toh wo alag-alag mudti hai.
Physics mein yeh kaise calculate karein ki light exactly kitne angle par mudegi?
Mental model
Mudne ka math = Snell's Law.
Sine of incoming angle (`i`) aur sine of outgoing angle (`r`) ka ratio hamesha fixed (constant) rehta hai. Yeh constant us material ki light ko modne ki taqat, yani 'Refractive Index', hota hai.
Explanation
Reflection ki tarah Refraction ke bhi do main laws hote hain. Pehla law kehta hai ki: incident ray, refracted ray, aur normal (surface ke `90-degree` wali imaginary line) sab ek hi plane (`2D` surface) mein hote hain.
Dusra law zyada important hai jise Snell's Law kehte hain. Yeh law incident angle (`i`) aur refracted angle (`r`) ke beech ek relation batata hai. Snell's law kehta hai ki: Ratio of sine of angle of incidence to the sine of angle of refraction ek constant hota hai. Mathematical form mein: `(sin i) / (sin r) = constant`.
Yahan `i` aur `r` normal (perpendicular) ke sath banaye gaye angles hote hain, surface ke sath nahi! Yeh ek bahut badi mistake point hai.
Yeh jo 'constant' nikalta hai, usko hum Refractive Index (`n` ya `mu`) bolte hain. Yeh refractive index hume batata hai ki medium kitna ghana (dense) hai aur wo light ko kitna zyada modekha. Agar `(sin i) / (sin r)` ki value badi aati hai, matlab material (jaise diamond) light ko bohot tezi se mod raha hai.
Worked example
Problem: Light travels from air into a transparent material. The angle of incidence is `45 degrees` and the angle of refraction is `30 degrees`. Calculate the refractive index of the material. (Given `sin 45° = 0.707`, `sin 30° = 0.5`)
- Snell's law ka formula likhein.
- Angles ki values daalein.
- Sine ki values substitute karein.
Answer: `n = 1.414`
Problem: For a given pair of media, the refractive index is `1.5`. If the sine of the angle of incidence is `0.6`, find the sine of the angle of refraction.
- Snell's law ki equation use karein.
- Equation ko rearrange karein taaki `sin r` nikal sake.
- Value calculate karein.
Answer: `sin r = 0.4`
Key points
- Snell's Law Formula: `(sin i) / (sin r) = constant` = refractive index (`n`).
- Angle Measurement: Angles `i` and `r` are ALWAYS measured from the Normal (the perpendicular line), not the surface.
Common mistakes
- Taking angle from the surface: Agar question bole 'light hits surface at `30 degrees`', toh bacche `i = 30` le lete hain. Normal se angle (`90 - 30 = 60`) hota hai, so `i = 60` hoga.
Recall questions
- What is Snell's Law?
- The constant in Snell's law is known as what?
- What happens to the ratio of `sin i` to `sin r` for a given color of light?
Questions & answers
A light ray enters from air to glass with an angle of incidence `60°`. If the refractive index of glass is `1.5`, what is the formula to find angle `r`?
`sin r = (sin 60°) / 1.5`
Approach: From Snell's law: `n = (sin i) / (sin r)`. Therefore, `sin r = (sin i) / n`.
If light enters from medium A to B and bends towards the normal, which medium has a higher refractive index?
Medium B has a higher refractive index because it is optically denser.
Approach: Compare bending direction to determine optical density.
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