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Physics Question 43 – JEE-MAIN 2025

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A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is _______.

When multiple lenses are placed in contact, their powers add up to give the power of the equivalent lens.

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Ninja Strategy•Diverging Lens Image Properties

First, calculate the equivalent focal length to determine if the combined system is converging or diverging. Then, use the known properties of image formation by such a lens for a real object to eliminate options.

Step 1: Calculate the equivalent focal length of the lens system✦ Active

The focal length of the convex lens is f1=+30 cm. The focal length of the concave lens is f2=−20 cm. For thin lenses in contact, the equivalent focal length F is given by:

1F=1f1+1f2

Substitute the given values:

1F=130+1−20=130−120=2−360=−160

Thus, the equivalent focal length is F=−60 cm. This indicates the combined system acts as a diverging lens.

Step 2: Apply the lens formula to find the image distance○ Expand

The object is placed at 20 cm to the left of the lens system, so the object distance is u=−20 cm (using Cartesian sign convention). Using the lens formula 1v−1u=1F:

1v−1−20=1−60

Simplify and solve for v:

1v+120=−160
1v=−160−120=−1−360=−460=−115

Therefore, v=−15 cm. The negative sign indicates that the image is formed on the same side as the object (to the left of the lens system). The distance of the image from the lens is 15 cm.

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