An object is placed at a distance of 2f from a concave mirror of focal length f. The image distance is

Question

BlackTom AI · Accepted Answer

We start by identifying the given quantities and the mirror type. The problem states a concave mirror with focal length f, and the object is placed at a distance 2f from the mirror. This means the object is located at the same distance as the center of curvature (since the center of curvature is 2f from the mirror).

Option a: 3f. If the object were located at 3f, the standard ray intersection for a concave mirror would place the image somewhere along the axis, but not at 3f in general. Since the question specifically ties the object to 2f, this option does not align with the given configuration.

Option b: 3f/2. At an object distance of 2f, standard image formation for a concave mirror does not yield an image distance of 3f/2. This value would imply a different object distance or a different focal length relationship than the one provided, making this option unlikely for the stated setup.

Option c: f. This would correspond to a scenario where the image lies at the focal plane, which happens for certain object distances (for example, objects at infinity produce images at f). With the object at 2f, the image position does not reduce to f according to the standard mirror behavior.

Option d: 2f. When an object is positioned at the center of curvature (distance 2f from the mirror) of a concave mirror, the image is formed at the same location as the object, i.e., also at 2f. The image is real, inverted, and of the same size as the object in this particular configuration, which matches the given 2f object distance.

To connect with the underlying principles: for a concave mirror, the mirror equation 1/f = 1/v + 1/u relates the focal length f, image distance v, and object distance u. If the object is at u = 2f (distance 2f in front of the mirror), then the standard result in this special case yields v = 2f, preserving the symmetry around the center of curvature. The other options imply image positions that correspond to different object placements or to misapplied relationships, making them inconsistent with the stated 2f object distance.

An object is placed at a distance of 2f from a concave mirror of focal length f. The image distance isSingle choice

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