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SMA Physics • Physics Lab Class XII • Exp 23

🪞 Refractive Index of Liquid (Concave & Plane Mirror)

📖 Manual
📐 Concave Mirror & Plane Mirror Liquid Setup
💡
Step 1 (Dry Mirror): Adjust needle height until its inverted image coincides with the needle tip at Center of Curvature $C \rightarrow h_1 = R = 30.0\text{ cm}$.
Step 2 (With Liquid & Plane Mirror Strip): Pour liquid into cavity. Coincide with plane mirror strip $\rightarrow h_0$, and with liquid-mirror combination $\rightarrow h_2$. Compute $\mu = \frac{h_1 - h_0}{h_2 - h_0}$.
Apparatus State:Dry Mirror (R = h₁)
Needle Height ($h$):30.0 cm
Coincidence Target:30.0 cm
Parallax Status:ZERO PARALLAX ✓
⚙️ Stand Height & Liquid Controls
1. Liquid & Plane Mirror Configuration
2. Needle Pointer Height ($h$) Range: 15 to 40 cm
Vertical Needle Height ($h$): 30.0 cm
Observer Eye Lateral Shift: Center
📊 Curvature & Liquid Refractive Index
Dry Curvature ($h_1 = R$)
30.0 cm
Strip Surface ($h_0$)
0.0 cm
Liquid Coincidence ($h_2$)
-- cm
Refractive Index ($\mu$)
--

📋 Observation Table: Refractive Index of Liquid (Concave & Plane Mirror)

Obs # Liquid Tested Real Curvature $h_1 = R$ (cm) Strip Surface $h_0$ (cm) Apparent Curvature $h_2$ (cm) Refractive Index $\mu = \frac{h_1 - h_0}{h_2 - h_0}$ Parallax Check
No observations logged yet. Find $h_1$ and $h_2$, then click "Record to Observation Table".
📈 Experimental Mean Result
Tested Liquid: Water
Mean Refractive Index $\mu$: --
🎯 Aim of the Experiment

To find the refractive index of a liquid using a concave mirror and a plane mirror.

📐 Working Formula
$$\mu = \frac{h_1 - h_0}{h_2 - h_0}$$

where:
• $h_1$ is the height of the needle tip from the pole of the dry concave mirror at its center of curvature $C$ ($R = h_1$).
• $h_0$ is the height of the plane mirror strip resting on the liquid surface from the mirror pole ($h_0 \approx 1.0\text{ cm}$, or $0$ for very thin layer).
• $h_2$ is the new coincidence height when rays refract through the liquid and reflect from the concave mirror.
If the liquid layer is very thin ($h_0 \approx 0$), the formula simplifies to:

$$\mu = \frac{h_1}{h_2} = \frac{R}{R'}$$
🔬 Physical Principle of Coincidence

When the needle tip is at height $h_2$, light rays entering the transparent liquid are refracted at the plane liquid surface toward the normal. If they strike the concave mirror normally along spherical radii, they reflect directly back along their incident paths. Upon re-emerging from the liquid surface into air, they refract back and re-converge to form an inverted real image coinciding tip-to-tip with the needle without parallax.

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