Focal Length of Lens in Water — Concept in 59 Seconds! 🔥

❓ Concept

🎬 Focal Length of Lens in Water — Concept in 59 Sec

Lens ko air se nikaal kar paani mein daal diya…
aur suddenly focal length change ho gaya? 🤔

👉 Isme koi magic nahi —
sirf relative refractive index ka game hai 🔥

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🖼️ Concept Image

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✍️ Short Explanation

JEE mein “lens in water” wale questions numerical kam, conceptual zyada hote hain.
Agar tum lens maker + relative refractive index samajh gaye,
toh answer seconds mein aa jaata hai 😎

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🔹 Step 1 — Lens Maker’s Formula (in Air)

For a thin lens in air:

$$\frac{1}{f_{\text{air}}}=({\mu }_{\text{lens}}-1)(\frac{1}{R_1}-\frac{1}{R_2})$$

Yahaan:

• $\mu_{\text{lens}}$ = refractive index of lens w.r.t air

• $R_1, R_2$ = radii of curvature

📌 Lens ka shape fixed hota hai — curvatures change nahi hote.

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🔹 Step 2 — Lens Placed in Another Medium

Agar lens ko kisi aur medium (jaise water) mein rakh diya:

👉 Refractive index relative ho jaata hai:

$${\mu }_{\text{relative}}=\frac{{\mu }_{\text{lens}}}{{\mu }_{\text{medium}}}$$

Modified lens maker formula:

$$\frac{1}{f_{\text{medium}}}=(\frac{{\mu }_{\text{lens}}}{{\mu }_{\text{medium}}}-1)(\frac{1}{R_1}-\frac{1}{R_2})$$

📌 Sirf μ change hota hai — geometry same rehti hai.

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🔹 Step 3 — Important Observation (VERY EXAM-FRIENDLY 🔥)**

• If $\mu_{\text{lens}} > \mu_{\text{medium}}$
  👉 lens converging rehta hai

• If $\mu_{\text{lens}} < \mu_{\text{medium}}$
  👉 lens diverging bhi ho sakta hai

📌 Isliye focal length ka sign bhi change ho sakta hai.

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🔹 Step 4 — Relation Between $f_{\text{air}}$ and $f_{\text{medium}}$**

Kyuki curvature term same hota hai:

$$\frac{1}{f_{\text{medium}}}\propto (\frac{{\mu }_{\text{lens}}}{{\mu }_{\text{medium}}}-1),\frac{1}{f_{\text{air}}}\propto ({\mu }_{\text{lens}}-1)$$

👉 Direct ratio se kaam ho jaata hai —
no need to re-derive formula every time 👍

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🔹 Step 5 — Concept Result (REMEMBER FOREVER ⭐)**

Lens ko denser medium mein daalne se:

• 🔻 Power kam hoti hai

• 🔺 Focal length badh jaati hai

🧠 One-line memory trick:

Denser medium → weaker lens

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⭐ Golden Summary Box (WRITE BOLD)

• Lens maker depends on relative refractive index

• Medium change ⇒ μ changes ⇒ power changes

• Geometry same ⇒ ratio method works

• Water (denser) ⇒ focal length increases

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✅ Final Takeaway

Is concept ko pakad liya,
👉 lens-in-water / lens-in-liquid questions JEE mein free marks ban jaate hain 🚀

No confusion, no ratta — pure physics logic.