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SMA Physics • Physics Lab Class XII • Exp 21

🔬 Refractive Index of Glass Slab (Travelling Microscope)

📖 Manual
📐 Travelling Microscope Stage & Eyepiece Field of View
💡
Stage 1: Focus cross-wires on the ink mark (P) on paper $\rightarrow$ Reading $R_1$.
Stage 2: Place glass slab over mark. Refocus on raised virtual image (P') $\rightarrow$ Reading $R_2$.
Stage 3: Focus on lycopodium powder on top face of slab $\rightarrow$ Reading $R_3$.
Current Stage:Stage 1: Mark (R₁)
Main Scale Reading (MSR):2.00 cm
Vernier Scale Coincidence (VSC):0 div
Total Reading (TR):2.000 cm
Cross-wire Focus:SHARP FOCUS ✓
⚙️ Vertical Height & Vernier Controls
1. Select Focusing Stage
2. Vertical Height (Coarse & Fine) LC = 0.001 cm
Coarse Height Adjustment: 2.000 cm
Fine Micrometer Screw (mm): 0.00 mm
Glass Slab Thickness ($t$): 1.80 cm
📊 Vernier & Depth Results
Paper Mark Reading (R₁)
2.000 cm
Apparent Mark Reading (R₂)
-- cm
Top Powder Reading (R₃)
-- cm
Refractive Index $\mu = \frac{R_3 - R_1}{R_3 - R_2}$
--

📋 Observation Table: Real & Apparent Depth of Glass Slab

Set # $R_1$ Mark (cm) $R_2$ Apparent (cm) $R_3$ Top (cm) Real Depth $(R_3 - R_1)$ cm Apparent Depth $(R_3 - R_2)$ cm Refractive Index $\mu = \frac{R_3 - R_1}{R_3 - R_2}$
No completed reading sets yet. Record $R_1, R_2, R_3$ to form a set.
📈 Final Experimental Results
Mean Real Thickness ($t$): -- cm
Mean Refractive Index ($\mu$): --
🎯 Aim of the Experiment

To determine the refractive index of a glass slab using a travelling microscope by measuring its real thickness and apparent thickness.

📐 Working Formula & Vernier Constant
$$\mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} = \frac{R_3 - R_1}{R_3 - R_2}$$

Least Count of Travelling Microscope:
$1\text{ Main Scale Division (MSD)} = 0.05\text{ cm} = 0.5\text{ mm}$
$50\text{ Vernier Scale Divisions (VSD)} = 49\text{ MSD}$
$$\text{Least Count (LC)} = 1\text{ MSD} - 1\text{ VSD} = \frac{1\text{ MSD}}{50} = \frac{0.05\text{ cm}}{50} = 0.001\text{ cm} = 0.01\text{ mm}$$

🔬 Why Apparent Depth is Less than Real Depth

When light rays originate from the ink mark on paper and travel through the denser glass slab into rarer air, they refract away from the normal. When produced backward, the rays appear to diverge from a virtual image located above the actual mark. The vertical apparent shift is given by: $$\Delta y = t\left(1 - \frac{1}{\mu}\right)$$

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