Correct Answer - Option 2 : 3.2 cm
The correct answer is option 2) i.e. 3.2 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:
The mirror used by dentists to obtain a magnified image is a concave mirror.
Given that:
Using sign convention - u, v and f will be negative
Object distance, u = -4 cm
Let image distance be -v
Magnification, m = 4
\(⇒ m =- \frac{v}{u} =4\)
⇒ v = -4u = -4(4) = -16 cm
Using mirror formula,
\( \frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
⇒ \( \frac{1}{-f} = \frac{1}{-16} + \frac{1}{-4}\)
⇒ \( \frac{1}{-f} = \frac{-20}{64 } =\frac{-5}{16}\)
⇒ \(f = \frac{16}{5} = 3.2 \: cm\)
