Correct Answer - Option 3 : (n+1)f/n
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 a focusing mirror/converging mirror.
- The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
- The concave mirror can form both real as well as virtual images of any object.
-
Mirror formula: The expression which shows the relation between object distance (u), image distance (v), and focal length (f) is called 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).
\(m = \frac{{{h_i}}}{{{h_o}}}\)
- The ratio of image distance to the object distance is called linear magnification.
\(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)
- A positive value of magnification means virtual an erect image.
- A negative value of magnification means a real and inverted image.
CALCULATION:
Given f = focal length and m = -n (negative sign shows that the image will be inverted to the object)
Since,
\(⇒m= {{h'} \over h}=\frac{-v}{u}=-n\)
⇒ v = nu -----(1)
The mirror formula is given as,
\(\Rightarrow \frac{1}{f}=\frac{1}{v}+\frac{1}{u}\) -----(2)
By equation 1 and equation 2,
\(\Rightarrow \frac{1}{f}=\frac{1}{nu}+\frac{1}{u}\)
\(\Rightarrow \frac{1}{f}=\frac{n+1}{nu}\)
\(\Rightarrow u=\frac{(n+1)}{n}f\)
- Hence, option 3 is correct.
