A concave mirror produces a three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Which option describes the image currently?

CONCEPT:

• Concave mirror: If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.
  • The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
  • The concave mirror can form both real as well as virtual images of any object.

• 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).

\(m = \frac{{{h_i}}}{{{h_o}}}\)

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

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

CALCULATION:

Given - m = 3 and object distance (u) = - 10 cm

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

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

\(⇒ 3 = -\frac{v}{-10}\)

⇒ m = -30 cm

• Here magnification is greater than 1, which means the image formed is enlarged, therefore an inverted image is formed at a distance of 30 cm in front of the given concave mirror. Therefore option 3 is correct.