Answer: 29 cm
Explanation:
The Focal length equation is:
[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}[/tex] (1)
Where:
[tex]f[/tex] is the focal length
[tex]u=39 cm[/tex] is the distance between the object and the convex lens
[tex]v[/tex] is the distance between the image and the convex lens
On the other hand, the magnification [tex]m[/tex] of the image is given by the following equation:
[tex]m=-\frac{v}{u}[/tex] (2)
Where [tex]m=-2.90[/tex] because the image is real, inverted and greater than the object
Finding [tex]v[/tex] from (2):
[tex]v=-m.u=-(-2.90)(39 cm)[/tex] (3)
[tex]v=113.1 cm[/tex] (4)
Substituting (4) in (1):
[tex]\frac{1}{f}=\frac{1}{39 cm}+\frac{1}{113.1 cm}[/tex] (5)
Finding [tex]f[/tex]:
[tex]\frac{1}{f}=\frac{1}{29}[/tex] (6)
[tex]f=29 cm[/tex] This is the focal length
