A concave mirror has a focal length 30 cm. The distance between the two position of the object

step 1 Okay, the question is a concave mirror has a focal length 30 cm. The distance between the two po

A concave mirror has a focal length 30 cm. The distance...

A concave mirror has a focal length $30 \mathrm{~cm}$. The distance between the two position of the object for which image size is double of the object is
(A) $30 \mathrm{~cm}$
(B) $15 \mathrm{~cm} \quad \overline{\text { (C) }-25 \mathrm{~cm}}$
(D) $-15 \mathrm{~cm}$

Key Concepts

Magnification

Magnification in mirrors is defined as the ratio of the image height to the object height, and it is also expressed as m = -di/do. The absolute value of magnification indicates how much larger or smaller the image is compared to the object. In problems where the image size is specified to be a certain multiple of the object size, this relationship is crucial for setting up the equations to solve for the object and image distances.

Multiple Object Positions and Quadratic Nature

Due to the quadratic nature of the mirror equation, the condition for a specific magnification (e.g., an image twice the size of the object) can be satisfied by two different object positions. This means that for the same mirror and magnification condition, the object can be placed at two distinct distances from the mirror, and the difference between these positions can be calculated by solving the resulting quadratic equation.

Concave Mirrors

Concave mirrors are curved reflecting surfaces that converge light rays to a focal point. They are used to produce real, inverted images when the object is positioned at appropriate distances from the mirror. The properties of concave mirrors depend on their curvature and focal length, which play a key role in determining the image position and size.

Mirror Equation

The mirror equation, given by 1/f = 1/do + 1/di, is a fundamental relationship in geometric optics. It connects the focal length of the mirror (f) with the object distance (do) and the image distance (di), allowing one to determine the position of the image formed by the mirror under various conditions of object placement.

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