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SMA Physics • Physics Lab Class XII • Exp 20

📐 Prism Angle of Minimum Deviation ($i-\delta$ Graph)

📖 Manual
📐 Equilateral Glass Prism Ray Tracing & Deviation Angle $\delta$
💡
Experiment Guide: Select the Angle of Incidence ($i$) between $30^\circ$ and $65^\circ$. Observe the refraction through the equilateral prism ($A = 60^\circ$). Note how the angle of deviation ($\delta$) decreases to a minimum $D_m \approx 37^\circ$ and then increases again!
Prism Angle $A$:60.0°
Incidence Angle $i$:48.0°
Refraction Angle $r_1$:30.0°
Emergence Angle $e$:48.0°
Deviation Angle $\delta$:36.0°
⚙️ Angle Controls & Snell's Law
1. Angle of Incidence $i$ Range: 32° to 65°
Incidence Angle ($i$): 48.0°
Prism Glass Material ($\mu$): Crown Glass (1.50)
📊 Refraction Data
First Surface $r_1$
29.7°
Second Surface $r_2$
30.3°
Angle of Emergence $e$
49.4°
Angle of Deviation $\delta = i + e - A$
37.4°

📋 Observation Table: Angle of Incidence vs Angle of Deviation

Obs # Prism Angle $A$ Angle of Incidence $i$ Angle $r_1$ Angle $r_2 = A - r_1$ Angle of Emergence $e$ Angle of Deviation $\delta = i+e-A$
No observations logged yet. Adjust incidence angle and click "Record to Observation Table".
📈 Minimum Deviation & Refractive Index Results
Angle of Minimum Deviation $D_m$: --°
Calculated Refractive Index $\mu$: --

📈 $i-\delta$ Characteristic Curve

The lowest point of the curve gives $D_m$.
🎯 Aim of the Experiment

To determine the angle of minimum deviation ($D_m$) for a given equilateral glass prism by plotting a graph between angle of incidence ($i$) and angle of deviation ($\delta$), and hence determine the refractive index ($\mu$) of the prism material.

📐 Governing Formulas
$$\delta = i + e - A$$ $$\text{At minimum deviation } (D_m): \quad i = e \quad \text{and} \quad r_1 = r_2 = \frac{A}{2}$$ $$\mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$
🔬 Key Characteristics of Minimum Deviation
  • The refracted ray passes parallel to the base of the equilateral prism.
  • The angle of incidence is equal to the angle of emergence ($i = e$).
  • The angles of refraction at the two surfaces are equal ($r_1 = r_2 = A/2 = 30^\circ$).
  • For an equilateral glass prism of $\mu = 1.50$, $D_m \approx 37.18^\circ$, giving $i \approx 48.59^\circ$.
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