The distance between the object and the image formed is 54 cm.
Step-by-step Explanation:Given: Focal length [tex]f[/tex] = 12 cm
magnification [tex]m[/tex] = -2 (negative sign for real image)
To Find: the distance between the object and the image formed
Solution:
- Finding the distance between the object and the image formed
The magnification [tex]m[/tex] is, [tex]m = \frac{v}{u} = -2[/tex] [tex]\Rightarrow v = -2u[/tex]
And, the lens formula is
[tex]\frac{1}{f} = \frac{1}{v} - \frac{1}{u}[/tex]
Substituting the given values in the above formula, we get;
[tex]\Rightarrow \frac{1}{12} = \frac{1}{(-2u)} - \frac{1}{u} = -\frac{1}{u} (\frac{3}{2})[/tex]
[tex]\Rightarrow u = -12 \times \frac{3}{2} = - 18 \ cm[/tex]
and, [tex]v = -2u = 36 \ cm[/tex]
The distance between the object and the image is [tex]v-u = 36+18=54 \ cm[/tex]
Hence, the distance between the object and the image formed is 54 cm.