Question:

If we want to obtain a real and magnified image of an object by using a concave mirror of focal length 18 cm. Where should the object be placed? Use mirror formula to determine the object distance for an image of magnification -2 by this mirror to justify your answer.

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For concave mirrors, the magnification and object distance can be related using the mirror formula. A negative magnification implies the image is real and inverted.
Updated On: May 19, 2025
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Solution and Explanation

Given:
Focal length \( f = 18 \, {cm} \)
Magnification \( M = -2 \)
We use the mirror formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where:
\( v \) is the image distance,
\( u \) is the object distance.
Also, magnification \( M \) is given by: \[ M = \frac{v}{u} \] Substitute \( M = -2 \): \[ -2 = \frac{v}{u} \quad \Rightarrow \quad v = -2u \] Now substitute \( v = -2u \) into the mirror equation: \[ \frac{1}{18} = \frac{1}{-2u} + \frac{1}{u} \] Simplify the equation: \[ \frac{1}{18} = \frac{-1 + 2}{u} \quad \Rightarrow \quad \frac{1}{18} = \frac{1}{u} \] Thus, \[ u = 18 \, {cm} \] So, the object should be placed 18 cm in front of the mirror to obtain the desired image.
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