Question

A 1 cm object is placed perpendicular to the principal axis of a convex mirror of focal length 7.5 cm. Find its distance from the mirror if the image formed is 0.6 cm in size.

Answer 1

Given,
Height of the object, h₁ = 1 cm
Focal length of the concave mirror, f = 7.5 cm = \[\frac{15}{2}  \text { cm }\]
Magnification is given as,

\[m =  - \frac{v}{u} = \frac{h_i}{h_0} = 0 . 6  \] 

\[\text{ Using  mirror  equation,} \] 

\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\] 

\[ \Rightarrow   \frac{1}{0 . 6u} - \frac{1}{u} = \frac{1}{f}\] 

\[ \Rightarrow   \frac{5}{3u} - \frac{1}{u} = \frac{2}{15}\] 

\[ \Rightarrow   u = 5  \text{ cm }\]
Hence, the distance of the object from the mirror is 5 cm.