A concave-convex lens has a refractive index of 1.5, and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. What will be the focal length of the liquid-glass combination?

 

🔍 Focal Length of a Lens with Liquid Combination – Optics | JEE Physics | Doubtify JEE

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📌 Question:

A concave-convex lens has a refractive index of 1.5, and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. What will be the focal length of the liquid-glass combination?

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🖼️ Question Image:

🧠 Solution Image:

🧪 Concept & Detailed Explanation:

✅ Key Formula:

The effective focal length of a lens with liquid combination is derived using a modified lens maker’s formula:

$$\frac{1}{f} = (\mu_{g}/\mu_{a} - 1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right) + (\mu_{l}/\mu_{a} - 1)\left( \frac{1}{R_2} \right)$$

Where:

• $\mu_g = 1.5$(glass)

• $\mu_l = 1.3$ (liquid)

• $\mu_a = 1.0$ (air)

• $R_1 = -30 \, \text{cm}$, $R_2 = +20 \, \text{cm}$
  

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🔢 Step-by-Step Calculation:

Using the standard lens maker’s formula with combination:

$$\frac{1}{f} = (1.5 - 1)\left( \frac{1}{-30} - \frac{1}{20} \right) + (1.3 - 1)\left( \frac{1}{20} \right)$$$$\frac{1}{f} = (0.5)\left( \frac{-1}{30} - \frac{1}{20} \right) + (0.3)\left( \frac{1}{20} \right)$$$$= 0.5\left( \frac{-1 - 1.5}{30} \right) + 0.3 \times \frac{1}{20} = 0.5 \times \left( -\frac{5}{60} \right) + \frac{0.3}{20} = -\frac{5}{120} + \frac{0.3}{20}$$$$= -\frac{1}{24} + \frac{3}{200} = -\frac{25}{600} + \frac{9}{600} = \frac{-16}{600} \Rightarrow f = \frac{-600}{16} = -37.5 \, \text{cm}$$

✅ Final Answer:

$$\boxed{f = -37.5 \, \text{cm}}$$

The negative sign indicates that the combination behaves like a concave lens.

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🎥 Video Solution:

🔍 Why This Question Is Important:

• Combines lens maker’s formula, refractive index, and compound lens systems

• Teaches handling non-standard setups like liquid-filled lens surfaces

• Frequently asked in JEE Mains & Advanced

• Enhances conceptual clarity on optical instruments and combinations

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🧠 Pro Tip:

Always remember:

When liquid is filled into a curved surface, treat it as another lens with its own refractive index acting at the surface.

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