Physics Q42 – JEE-MAIN 2025

A lens having refractive index

1.6

has focal length of

12 cm

, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as

1.28

)

Clue 1 of 3: Conceptual Principle

The focal length of a lens changes when it is immersed in a medium other than air, as it depends on the refractive index of the surrounding medium.

🥷

Ninja Strategy•Estimate Factor of Change

Recognize that the focal length increases when the lens is placed in a denser medium (but still less dense than the lens material), and quickly estimate the factor of increase using the ratio of $(n_{l e n s} / n_{m e d i u m} - 1)$ terms.

🧠 Full Solution Path

Step 1: Determine the curvature term of the lens✦ Active

The Lens Maker's Formula is given by $\frac{1}{f} = (\frac{n_{l e n s}}{n_{m e d i u m}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ . Let $n_{g}$ be the refractive index of the lens, $n_{a}$ for air, and $n_{w}$ for water. Let $K = (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ be the curvature term. Given $n_{g} = 1.6$ , $f_{a} = 12 cm$ , and $n_{a} = 1$ (for air).

\frac{1}{f_{a}} = (\frac{n_{g}}{n_{a}} - 1) K

\frac{1}{12} = (\frac{1.6}{1} - 1) K

\frac{1}{12} = (0.6) K

K = \frac{1}{12 \times 0.6} = \frac{1}{7.2}

Step 2: Calculate the focal length in water○ Expand

Now, we use the Lens Maker's Formula for the lens placed in water. Given $n_{w} = 1.28$ .

\frac{1}{f_{w}} = (\frac{n_{g}}{n_{w}} - 1) K

\frac{1}{f_{w}} = (\frac{1.6}{1.28} - 1) \times \frac{1}{7.2}

\frac{1.6}{1.28} = \frac{160}{128} = \frac{5}{4} = 1.25

\frac{1}{f_{w}} = (1.25 - 1) \times \frac{1}{7.2}

\frac{1}{f_{w}} = (0.25) \times \frac{1}{7.2}

\frac{1}{f_{w}} = \frac{1}{4} \times \frac{1}{7.2} = \frac{1}{28.8}

f_{w} = 28.8 cm

Step 3: Convert the focal length to millimeters○ Expand

The options are given in millimeters. Convert the calculated focal length from centimeters to millimeters.

f_{w} = 28.8 cm \times 10 \frac{mm}{cm} = 288 mm

💡 Teacher's Secret Hint

Always check the units required in the options before finalizing your answer.

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Physics Question 42 – JEE-MAIN 2025

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path