Correct Answer - Option 1 : 15 cm in front of 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.
