Correct Answer - Option 1 : 22.5 cm
The correct answer is option 1) i.e. 22.5 cm
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.
CALCULATION:
Given that:
Focal length, f = 15 cm
The image is two times the size of the object.
∴ Magnification, m = -2
Let the image distance from the mirror be v and the object distance from the mirror be u.
Using sign convention, f = -15 cm
\(⇒ m =- \frac{v}{u} \)
\(⇒ -2 = - \frac{v}{u} \)
⇒ v = 2u
Using the mirror formula,
\(⇒ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
\(⇒ \frac{1}{-15} = \frac{1}{2u} + \frac{1}{u}\)
\(⇒ \frac{1}{-15} = \frac{3}{2u}\)
⇒ u = - 22.5 cm
- Therefore, the distance between the object and the mirror is 22.5 cm.