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A convex lens forms a real and inverted image of an object placed at 2F. Where is the image formed?
At F
At 2F
Between F and 2F
Beyond 2F
At 2F
When an object is placed at the 2F position of a convex lens, the image is formed exactly at the 2F position on the other side of the lens. The image formed is real, inverted, and of the same size as the object.
When an object is placed at the 2F position of a convex lens, the image is formed exactly at the 2F position on the other side of the lens. The image formed is real, inverted, and of the same size as the object.
Think of it as a perfectly balanced scale; at 2F, the object and its image have a 1:1 ratio, just like placing equal weights on both sides of a beam balance.
At 2F, you get 2F: Same size, real, and inverted.
f1тАЛ=v1тАЛтИТu1тАЛ тАФ Lens formula relating focal length, object distance, and image distance
m=uvтАЛ=hoтАЛhiтАЛтАЛ тАФ Magnification formula
This occurs because the magnification m for a convex lens is defined as m=uvтАЛ. When u=тИТ2F and v=+2F, the magnification becomes m=тИТ2F2FтАЛ=тИТ1. The negative sign indicates an inverted image, and the magnitude of 1 signifies that the object height and image height are identical.
At 2F, the object distance equals the image distance (тИгuтИг=тИгvтИг).
The magnification is exactly тИТ1.
This position is often used to demonstrate the inversion property of convex lenses.
Produces an image identical in size to the original object
Maintains clear geometric projection
Requires precise placement at exactly twice the focal length
Sensitive to lens aberrations if the aperture is too large
Used in photography for 1:1 macro reproduction
Used in optical instruments for image inversion and size calibration
Focal length f is a constant property of the lens determined by the refractive index and radius of curvature.
Option A (AtF) occurs when the object is at infinity. Option C (Between F and 2F) occurs when the object is beyond 2F. Option D (Beyond 2F) occurs when the object is between F and 2F.
B is correct тАФ When an object is placed at 2F in front of a convex lens, the real and inverted image is formed at 2F on the other side with identical size.
Always remember that for a convex lens, moving an object towards the lens pushes the image further away; they 'cross' each other at the 2F position.
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