A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?

Understanding Image Formation: In optics, the way a mirror forms an image of an object depends on the type of mirror and the position of the object relative to the mirror. Concave mirrors, in particular, can produce various types of images based on these factors.

Properties of Concave Mirrors: A concave mirror is a spherical mirror that curves inward. It is capable of producing real, inverted images when the object is placed outside the focal point, and virtual, erect images when the object is within the focal point.

Object Placement and Image Magnification: In the given scenario, an object is placed 10 cm in front of a concave mirror, and a real image that is three times magnified (enlarged) is produced. This indicates that the object is placed between the focal point and the center of curvature of the mirror.

Applying Optical Principles: The relationship between object distance (u), image distance (v), and magnification (m) in mirror optics is given by m = −v/u. Here, magnification is positive for virtual images and negative for real images. Given
m = 3 and u = −10 cm (object distance is taken as negative in the mirror formula), we can find the image distance.

Determining Image Location: Substituting the given values into the magnification formula, 3 = −v/−10, we can solve for v. This calculation gives v = −30 cm, indicating that the image is formed 30 cm in front of the mirror.

Image Position in Concave Mirror: Therefore, in this scenario, the concave mirror forms a real, magnified image 30 cm in front of it. This distance reflects the specific properties of the concave mirror and the object’s position relative to it.

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