Refraction through a Prism 🔺

Setup 🧭

Think of a triangular glass prism ABC. A light ray PQ hits the first face AB with angle of incidence i and bends to angle r₁. Inside, it meets the second face AC with angle r₂ and finally leaves with angle of emergence e. The gap between the original and final directions is the angle of deviation d. :contentReference[oaicite:0]{index=0}

Angle relationships ✍️

• Inside the little quadrilateral geometry, the bending angles add up neatly to \( r_1 + r_2 = A \)  (Equation 9.34). :contentReference[oaicite:1]{index=1}

Total deviation d 🎯

A prism bends the ray twice, so the grand total turn is \( d = i + e – A \)  (Equation 9.35). :contentReference[oaicite:2]{index=2}

Deviation-versus-Incidence curve 📈

If you draw d against i, the graph dips to a single lowest point called the minimum deviation D_m. Every deviation (except at that dip) comes from two possible incidence angles because the curve is symmetric. :contentReference[oaicite:3]{index=3}

Minimum deviation shortcut ⭐

• At the special position D_m you get i = e and r₁ = r₂; the inside ray runs parallel to the prism’s base. :contentReference[oaicite:4]{index=4}
• From the geometry: \( r = \tfrac{A}{2} \)  (Equation 9.36). :contentReference[oaicite:5]{index=5}
• And the handy link: \( D_m = 2i – A \) ⇨ \( i = \tfrac{A + D_m}{2} \)  (Equation 9.37). :contentReference[oaicite:6]{index=6}

Finding the refractive index n 👓

Grab the apex angle A and the measured D_m, then pop them into \[ n_{21} \;=\; \frac{\sin\!\bigl[(A + D_m)/2\bigr]}{\sin(A/2)} \] (Equation 9.38). :contentReference[oaicite:7]{index=7}

Thin-prism hack ✂️

When the prism is skinny (A small), both A and D_m shrink, giving the quick rule \[ D_m \;\approx\; (n_{21} – 1)A \] so a thin prism nudges the ray only a little. :contentReference[oaicite:8]{index=8}

High-yield ideas for NEET 🚀

1. Minimum-deviation condition with \( r = A/2 \).
2. Refractive-index formula \( n_{21} = \sin[(A + D_m)/2] / \sin(A/2) \).
3. Thin-prism shortcut \( D_m ≈ (n_{21} – 1)A \).
4. Total deviation relation \( d = i + e – A \).
5. Shape of the d-versus-i graph and why it has a single minimum.

Keep these nuggets handy and you’ll ace prism questions with confidence! 💡✨