Physics Q41 – JEE-MAIN 2026

An object AB is placed

15

cm on the left of a convex lens P of focal length

10

cm. Another convex lens Q is now placed

15

cm right of lens P. If the focal length of lens Q is

15

cm, the final image is _______.

Clue 1 of 3: Two-Lens System

For a system of two lenses, the image formed by the first lens acts as the object for the second lens.

🧠 Full Solution Path

Step 1: Image formation by Lens P✦ Active

For convex lens P, the focal length is $f_{P} = + 10$ cm. The object distance is $u_{P} = - 15$ cm (object on the left). Using the lens formula $\frac{1}{v_{P}} - \frac{1}{u_{P}} = \frac{1}{f_{P}}$ :

\frac{1}{v_{P}} - \frac{1}{- 15} = \frac{1}{10} ⟹ \frac{1}{v_{P}} = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}

So, $v_{P} = + 30$ cm. The image $I_{1}$ is real, inverted, and formed $30$ cm to the right of lens P. The magnification is $m_{P} = \frac{v_{P}}{u_{P}} = \frac{30}{- 15} = - 2$ .

Step 2: Object for Lens Q○ Expand

Lens Q is placed $15$ cm to the right of lens P. The image $I_{1}$ is formed $30$ cm to the right of lens P. Therefore, the distance of $I_{1}$ from lens Q is $30 cm - 15 cm = 15 cm$ . Since $I_{1}$ is to the right of lens Q, it acts as a virtual object for lens Q. Thus, the object distance for lens Q is $u_{Q} = + 15$ cm. The focal length of convex lens Q is $f_{Q} = + 15$ cm.

💡 Teacher's Secret Hint

Remember that a virtual object has a positive object distance.

Step 3: Final image formation by Lens Q○ Expand

Using the lens formula for lens Q: $\frac{1}{v_{Q}} - \frac{1}{u_{Q}} = \frac{1}{f_{Q}}$

\frac{1}{v_{Q}} - \frac{1}{+ 15} = \frac{1}{15} ⟹ \frac{1}{v_{Q}} = \frac{1}{15} + \frac{1}{15} = \frac{2}{15}

So, $v_{Q} = + 7.5$ cm. The final image is real (since $v_{Q} > 0$ ) and formed $7.5$ cm to the right of lens Q. The magnification by lens Q is $m_{Q} = \frac{v_{Q}}{u_{Q}} = \frac{7.5}{15} = + \frac{1}{2}$ . The total magnification is $M = m_{P} \times m_{Q} = (- 2) \times (+ \frac{1}{2}) = - 1$ . This means the final image is real, formed $7.5$ cm right of lens Q, and has the same size as the object AB (magnitude of magnification is 1). This matches option 2.

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Physics Question 41 – JEE-MAIN 2026

Clue 1 of 3: Two-Lens System

🧠 Full Solution Path