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Refraction at Spherical Surface | Complete Derivation for JEE, NEET & Class 12 Physics

In this video, we study one of the most important topics of Ray Optics — Refraction at a Spherical Surface.
This concept is the foundation of all lens formulas, image formation, optical instruments, and ray diagrams. If you understand this one topic deeply, half of ray optics becomes easy.

This lecture is specially designed for:
• JEE Main
• JEE Advanced
• NEET
• Class 12 CBSE
• Boards + Olympiads

Students across India find this topic confusing because most teachers jump directly to the formula:

\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}

without showing where it actually comes from.

In this video, you will learn the complete derivation step-by-step from geometry and Snell’s law, exactly the way Kota coaching faculty and top rankers learn it.

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🔥 Why This Topic Is Extremely Important

Refraction at a spherical surface is the starting point of all lens theory.

From this formula we derive:
• Thin lens formula
• Lens maker’s formula
• Magnification
• Power of lens
• Optical instruments
• Microscopes
• Telescopes
• Human eye corrections

So if you skip this concept, everything later becomes mechanical and confusing.

But if you master this derivation, ray optics becomes logical instead of memorization.

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📘 What Is Refraction at a Spherical Surface?

Whenever light travels from one medium to another through a curved surface, refraction happens.

Examples:
• Light entering a glass lens from air
• Light coming out of water into air
• Light passing through eye lens

All these involve spherical surfaces.

So we need a formula that connects:
• Object distance (u)
• Image distance (v)
• Radius of curvature (R)
• Refractive indices (n₁ and n₂)

That formula is:

\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}

But instead of memorizing, we derive it from pure physics.

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📐 Step-by-Step Derivation Explained in This Video

In this lecture, we do:
1. Draw a proper ray diagram
2. Define:
• Pole (P)
• Center of curvature (C)
• Normal (N)
3. Apply Snell’s law
4. Use small angle approximation
5. Convert everything into:
• u
• v
• R
6. Simplify to get the final formula

This is exactly how questions are solved in:
• JEE Main
• NEET
• Boards
• Olympiads

No shortcut. No skipping steps.

Only concept + logic + mathematics.

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🧠 Why Most Students Fail This Topic

Students fail because they:

❌ Memorize the formula
❌ Forget sign conventions
❌ Cannot draw proper ray diagram
❌ Don’t know which distances are positive or negative
❌ Don’t understand normal direction

This video fixes all of that.

After watching this lecture, you will be able to:
• Derive the formula on your own
• Apply it to convex and concave surfaces
• Solve numericals confidently
• Connect it with lenses

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🧪 Applications Covered

After this topic, you can understand:
• Convex lens
• Concave lens
• Glass slabs
• Contact lenses
• Camera lenses
• Microscope
• Telescope
• Eye optics

Everything in optics is built on this one formula.

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🏆 Designed for Rankers

This video is taught in coaching-style chalkboard format, similar to Kota, Allen, Resonance, NV Sir style, where clarity and derivation matter more than fancy animation.

It is made for:
• Serious JEE aspirants
• NEET toppers
• Board exam students
• Physics lovers

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📚 Who Should Watch This?

You must watch this if you are:
• In Class 12 Physics
• Preparing for JEE
• Preparing for NEET
• Revising Ray Optics
• Weak in derivations
• Confused about lens formulas

Even if you have studied this before, watching this once will clear your concepts permanently.

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🧩 What You Will Master After This Video

After watching this full lecture, you will be able to:

✔ Derive the spherical refraction formula
✔ Apply it in any numerical
✔ Use correct sign convention
✔ Understand ray diagrams
✔ Connect it with lens theory
✔ Solve advanced JEE problems

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🧠 Formula You Will Never Forget

Because it is derived logically, not memorized:

\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}

Once you understand this, no optics formula will scare you again.

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🎯 This Lecture Will Increase Your Marks

This topic gives:
• 2–4 marks in JEE
• 3–5 marks in NEET
• 5–8 marks in Boards

So mastering it is directly equal to higher rank and better college.

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📌 Watch Till the End

Do not skip.

The real magic happens when all steps combine and the formula appears.

This is how physics should be learned — with logic, not memorization.

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🔔 Subscribe for More Physics

This channel focuses on:
• Conceptual Physics
• JEE + NEET
• Ray Optics
• Derivations
• Problem solving
• Rank-oriented teaching

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📈 If You Want to Score High in Physics…

Start with strong foundations.
This video gives you exactly that.

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📌 Topic Covered:

Refraction at Spherical Surface
Ray Optics
Class 12 Physics
JEE Main
JEE Advanced
NEET
Derivation
Optics