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SMA Physics • Physics Lab Class XII • Exp 22

💧 Refractive Index of Liquid (Liquid Lens Method)

📖 Manual
📐 Vertical Stand: Convex Lens, Plane Mirror & Plano-Concave Liquid Lens
💡
Step 1 (Dry Lens): Move needle vertically until its inverted reflection coincides with its tip $\rightarrow$ Focal length $f_1$.
Step 2 (With Liquid): Toggle Liquid ON. The liquid drop forms a plano-concave lens. Refocus needle $\rightarrow$ Combination focal length $F$.
Liquid Status:No Liquid (Dry Lens f₁)
Needle Height ($h$):20.0 cm
True Focus:20.0 cm
Parallax Status:ZERO PARALLAX ✓
⚙️ Stand Height & Liquid Controls
1. Liquid Layer & Medium
2. Needle Height ($h$) Range: 15 to 45 cm
Vertical Pointer Height ($h$): 20.0 cm
Observer Eye Lateral Shift: Center
📊 Focal Length & Liquid Refractive Index
Dry Lens Focal Length ($f_1$)
20.0 cm
Combination Focal Length ($F$)
-- cm
Liquid Lens Focal Length ($f_2$)
-- cm
Liquid Refractive Index ($\mu$)
--

📋 Observation Table: Refractive Index of Liquid

Obs # Liquid Tested Dry Lens $f_1$ (cm) Combination $F$ (cm) Liquid Lens $f_2 = \frac{f_1 F}{f_1 - F}$ (cm) Radius of Curvature $R$ (cm) Refractive Index $\mu = 1 - \frac{R}{f_2}$
No observations logged yet. Find $f_1$ and $F$, 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 convex lens and a plane mirror.

📐 Working Formulas
$$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \implies \frac{1}{f_2} = \frac{1}{F} - \frac{1}{f_1} \implies f_2 = \frac{f_1 \cdot F}{f_1 - F}$$ $$\text{Plano-concave lens formula: } \quad \frac{1}{f_2} = (\mu - 1)\left(-\frac{1}{R}\right) \implies \mu = 1 - \frac{R}{f_2} = 1 + \frac{R}{|f_2|}$$

where $f_1$ is the focal length of the convex lens, $F$ is the focal length of the lens-liquid combination, $f_2$ is the focal length of the plano-concave liquid lens, and $R$ is the radius of curvature of the lower face of the convex lens.

🔬 Why Coincidence Occurs at Focus

When the object needle is at the principal focus of the lens system, the rays refracted by the lens become parallel. These parallel rays strike the horizontal plane mirror normally and are reflected back along their original paths. Refracting through the lens again, they converge to form an inverted real image right at the position of the needle tip without parallax.

❓ Viva Voce Interactive Quiz