Correct Answer - Option 2 :
\(-\frac{f}{p}\)
The correct answer is option 2) i.e. \(-\frac{f}{p}\)
CONCEPT:
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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
\(⇒ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
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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.
EXPLANATION:
Since the image formed is real, the object is placed behind the focal point. Hence, object distance, u = -(f + p)
Using mirror formula, \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
\(\frac{1}{-f} = \frac{1}{-v} + \frac{1}{-(f+p)}\) (Using sign convention: f,v, and u are negative)
\(\Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{(f+p)}\)
\(\Rightarrow {v} = \frac{f(f+p)}{p}\)
The ratio of the size of the real image to the size of the object is magnification.
Magnification, \( m = \frac{-v}{u} = -\frac{-[\frac{f(f+p)}{p}]}{-[f+p]} = -\frac{f}{p}\)
