Correct Answer - Option 4 : 120 cm
CONCEPT:
Mirror
- A mirror is a polished surface that reflects the light incident on it.
- Types of the mirror:
- Plane mirror
-
Spherical mirror
- Concave mirror
- Convex mirror
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).
\(⇒ m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}\)
CALCULATION:
Given f = -80 cm, and \(\frac{h_{i}}{h_{o}}=-2\)
Where hi = height of the image, and ho = height of the object
- The magnification of the mirror is given as,
\(⇒ m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}\)
\(⇒ v=-u×\frac{h_{i}}{h_{o}}\)
\(⇒ v=-u×\frac{(-2)}{1}\)
⇒ v = 2u -----(1)
According to the mirror formula,
\(⇒ \frac{1}{f}=\frac{1}{u}+\frac{1}{v}\) -----(2)
Where u = distance of the object from the mirror, v = distance of the image from the mirror, and f = focal length
By equation 1 and equation 2,
\(⇒ \frac{1}{f}=\frac{1}{u}+\frac{1}{2u}\)
\(⇒ \frac{1}{-80}=\frac{3}{2u}\)
⇒ u = -120 cm
- Hence, option 4 is correct.