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.

Hint:

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.

Answer 1

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 defined as: \[M = \frac{v}{u}\] Substitute \( M = -2 \): \[-2 = \frac{v}{u} \quad \Rightarrow \quad v = -2u\] Substitute \( v = -2u \) into the mirror equation: \[\frac{1}{18} = \frac{1}{-2u} + \frac{1}{u}\] Simplify: \[\frac{1}{18} = \frac{-1 + 2}{u} \quad \Rightarrow \quad \frac{1}{18} = \frac{1}{u}\] Therefore, \[u = 18 \, {cm}\] The object should be positioned 18 cm in front of the mirror to achieve the required image.