Physics Q41 – JEE-MAIN 2026

A spherical interface lens of radius

R

separates two media of refractive indices

1

and

1.4

respectively as shown in the figure below. A point source is placed at a distance of

4 R

in front of spherical interface. The magnitude of the magnification of point source image is _______.

Clue 1 of 3: Refraction at Spherical Surface

Identify the given parameters: refractive indices of the two media, object distance, and radius of curvature.

🧠 Full Solution Path

Step 1: Apply Spherical Refraction Formula✦ Active

Given refractive indices $n_{1} = 1$ and $n_{2} = 1.4$ . The object is placed at a distance $4 R$ in front of the spherical interface, so the object distance is $u = - 4 R$ . The interface is convex from the left, so the radius of curvature $R$ is positive. The formula for refraction at a spherical surface is:

\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}

Substitute the given values:

\frac{1.4}{v} - \frac{1}{- 4 R} = \frac{1.4 - 1}{R}

Step 2: Calculate Image Distance○ Expand

Simplify the equation to find the image distance $v$ :

\frac{1.4}{v} + \frac{1}{4 R} = \frac{0.4}{R}

Rearrange and solve for $v$ :

\frac{1.4}{v} = \frac{0.4}{R} - \frac{1}{4 R} = \frac{1.6}{4 R} - \frac{1}{4 R} = \frac{0.6}{4 R}

Therefore,

v = \frac{1.4 \times 4 R}{0.6} = \frac{5.6 R}{0.6} = \frac{56 R}{6} = \frac{28 R}{3}

💡 Teacher's Secret Hint

Ensure correct algebraic manipulation and common denominators when combining terms.

Step 3: Calculate Magnitude of Magnification○ Expand

The transverse magnification $m$ for refraction at a spherical surface is given by:

m = \frac{n_{1} v}{n_{2} u}

Substitute the values of $n_{1}$ , $n_{2}$ , $u$ , and $v$ :

m = \frac{(1) (\frac{28 R}{3})}{(1.4) (- 4 R)} = \frac{\frac{28 R}{3}}{- 5.6 R} = \frac{28}{3 \times (- 5.6)} = \frac{28}{- 16.8} = - \frac{280}{168} = - \frac{5}{3}

The magnitude of the magnification is $| m | = | - \frac{5}{3} | = \frac{5}{3} \approx 1.666 . . .$ which rounds to $1.66$ .

💡 Teacher's Secret Hint

Remember that magnification can be negative, indicating an inverted image. The question asks for the magnitude.

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Physics Question 41 – JEE-MAIN 2026

Clue 1 of 3: Refraction at Spherical Surface

🧠 Full Solution Path