A convex mirror has a focal length ‘f’ and it can produce an imag

SOLUTION

CONCEPT:

Mirror

• A mirror is a polished surface that reflects the light incident on it.
• Types of the mirror:
  1. Plane mirror
  2. Spherical mirror
     • ​​Concave mirror
     • Convex mirror

CALCULATION:

Given f = f and \(h_{I}=\frac{1}{n}h_{O}\)

Where h_I = height of image and h_O = height of the object

• Mirror formula is written as,

\(⇒ \frac{1}{u}+\frac{1}{v}=\frac{1}{f}\)     -----(1)

Where u = distance of the object from the mirror, v = distance of the image from the mirror, and f = focal length

• The f and v are taken as positive and u is taken as negative for the convex mirror.​
• The magnification of the mirror is given as,

\(\Rightarrow m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}\)

• For the given mirror,(u will be taken as negative)

\(\Rightarrow \frac{v}{u}=-\frac{1}{n}\)

\(\Rightarrow v=-\frac{u}{n}\)     -----(2)

• By equation 1 and equation 2,(u will be taken as negative)

\(⇒ \frac{1}{u}+\frac{n}{-u}=\frac{1}{f}\)

\(⇒ \frac{1}{u}-\frac{n}{u}=\frac{1}{f}\)

\(⇒ \frac{1-n}{u}=\frac{1}{f}\)

\(⇒ u=f(1-n)\)

\(⇒ u=-f(n-1)\)

• Hence, option 4 is correct.