A concave mirror forms 3 times magnified real, inverted image of an object kept at 5 cm in front of mirror. Find the distance of image from the mirror.

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 the converging mirror.
• The nature of the image formed by a concave mirror is real and inverted except when the object is kept between the focus and pole, where the image is virtual and erect.
• The relation between object distance (u) and image distance (v) with focal length (f) is given by the mirror equation or mirror formula.

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

​Magnification

• It is the ratio of the image distance (v) and object distance (u)
• ​Mathematically it is written as

\(⇒ m = \frac{-v}{u} = \frac{h'}{h}\)

Where h' is the height of the image and h is the height of the object.

Sign Convention

• The left-hand side of the mirror is considered negative. 
• The object is always kept on the left-hand side of the mirror that is the negative side. 
• The above the mirror is positive and below the mirror is negative. 
• So, if the real and inverted image is formed magnification is negative and if the erect image is formed the magnification is positive. 

​Calculation:

The image is inverted, so magnification is negative. It is three times magnified, So magnification m is

m = 3

Object distance u = - 5 cm

Image distance v

By formula of magnification,

\( m = \frac{-v}{u}\)

⇒ v = 3 u = 3 × - 5 cm = - 15 cm

So, the image is formed 15 cm in front of the mirror.