Correct Answer - Option 2 : 6.67 cm
Concept:
Mirror
- A mirror is a polished surface that reflects the light incident on it.
- Types of the mirror:
- Plane mirror
- Spherical mirror
- Spherical Mirror includes a concave mirror and convex Mirror
Concave and Convex Mirror
- Concave mirrors have reflecting surface inward and the convex mirror has reflecting surface outward.
- The concave mirror has a focus toward which it converges reflecting rays falling on it parallel to principal axis.
- Convex mirror diverges ray of light falling on it such that it appears to be coming from an imaginary point beyond it known as focus.
- The distance between the mirror and its focus is called the focal length.
Mirror formula:
- The expression which shows the relation between object distance (u), image distance (v), and focal length (f) is called the 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).
\(⇒ m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}\)
Sign Convention for mirror
- The left side of the mirror, where the object is placed is considered as positive and behind the mirror negative.
- Erect objects are considered positive and inverted as negative.
- The focal length for the concave mirror is negative and the convex mirror is positive.
Calculation:
Given, the image distance v = - 20 cm (in front of mirror is negative distance)
focal length f = ?
Magnification m = - 2 (real image so inverted, so magnification will be with minus sign)
\(⇒ - 2 = -\frac{v}{u}\)
⇒ v = 2u
v = - 20cm, So u = - 10 cm
So, object is kept 10 cm infornt of mirror
Now, applying mirror formula
\(⇒\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
\(⇒\frac{1}{-20} + \frac{1}{-10} = \frac{1}{f}\)
\(⇒ f = \frac{1+2}{-20} = -\frac{20}{3}\)
⇒ f = - 6.67 cm
The minus sign indicates it is in front of the mirror.
So, the focal length is 6.67 cm.
