Physics Q50 – JEE-MAIN 2025

A container contains a liquid with refractive index of

1.2

up to a height of

60

cm and another liquid having refractive index

1.6

is added to height

H

above first liquid. If viewed from above, the apparent shift in the position of bottom of container is

40

cm. The value of

H

is _______ cm. (Consider liquids are immiscible)

Enter Calculated Numerical Value:

Clue 1 of 3: Apparent Shift Concept

When an object is viewed through a medium of different refractive index, its apparent position shifts.

🧠 Full Solution Path

Step 1: Identify Given Parameters and Formula✦ Active

We are given two immiscible liquid layers. For the first liquid, height $h_{1} = 60$ cm and refractive index $n_{1} = 1.2$ . For the second liquid, height $h_{2} = H$ cm and refractive index $n_{2} = 1.6$ . The total apparent shift in the position of the bottom of the container, when viewed from above, is $S_{t o t a l} = 40$ cm. The formula for apparent shift $S$ due to a single layer of thickness $h$ and refractive index $n$ (when viewed from air) is $S = h (1 - \frac{1}{n})$ . For multiple layers, the total shift is the sum of individual shifts.

Step 2: Calculate Individual Shifts○ Expand

The shift due to the first liquid layer ( $S_{1}$ ) is:

S_{1} = h_{1} (1 - \frac{1}{n_{1}}) = 60 (1 - \frac{1}{1.2}) = 60 (1 - \frac{10}{12}) = 60 (1 - \frac{5}{6}) = 60 (\frac{1}{6}) = 10 cm

The shift due to the second liquid layer ( $S_{2}$ ) is:

S_{2} = h_{2} (1 - \frac{1}{n_{2}}) = H (1 - \frac{1}{1.6}) = H (1 - \frac{10}{16}) = H (1 - \frac{5}{8}) = H (\frac{3}{8})

💡 Teacher's Secret Hint

Ensure correct calculation of the term $(1 - 1 / n)$ for each liquid.

Step 3: Sum Shifts and Solve for H○ Expand

The total apparent shift is the sum of the individual shifts:

S_{t o t a l} = S_{1} + S_{2}

Substitute the given total shift and the calculated individual shifts:

40 = 10 + H (\frac{3}{8})

Now, solve for $H$ :

30 = H (\frac{3}{8})

H = 30 \times \frac{8}{3}

H = 10 \times 8

H = 80 cm

💡 Teacher's Secret Hint

Double-check the algebraic manipulation to isolate H.

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Physics Question 50 – JEE-MAIN 2025

Clue 1 of 3: Apparent Shift Concept

🧠 Full Solution Path