Answer:
the image is -38.7 cm from the lens
Explanation:
We use the lens equation which says
[tex]$\frac{1}{u}+\frac{1}{v}=\frac{1}{f} $[/tex]
where [tex]u[/tex] is the distance to the object, [tex]v[/tex] is the distance to the image, and [tex]f[/tex] is the focal length.
Now, in our case
[tex]u =18.6cm[/tex],
[tex]v= 35.8cm[/tex],
[tex]f = 35.8cm[/tex];
therefore,
[tex]$\frac{1}{18.6}+\frac{1}{v}=\frac{1}{35.8} $[/tex]
[tex]$\frac{1}{v}=\frac{1}{35.8}-\frac{1}{18.6} $[/tex]
[tex]\boxed{v=-38.7cm}[/tex]
where the negative sign indicates that the image is virtual and on the same side of the lens as the object.
