An object is placed 100 cm in front of a concave mirror. The real image of the object is formed 50 cm in front of the mirror. What is the object's magnification ?

CONCEPT:

• Mirror formula: The expression which shows the relation between object distance (u), image distance (v), and focal length (f) is called mirror formula.

\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)

Linear magnification (m):

• It is defined as the ratio of the height of the image (hi) to the height of the object (ho).

i.e. \(m = \frac{{{h_i}}}{{{h_o}}}\)

• The ratio of image distance to the object distance is called linear magnification.

i.e. \(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)

CALCULATION:

Given - u = -100 cm and v = -50 cm

• As we know that the ratio of image distance to the object distance is called linear magnification.

 \(\Rightarrow m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)

\(\Rightarrow m = -\frac{-50}{-100}=-0.5\)