Answer:
Focal Length = 38.61cm, Power = 2.59 Diopter, Converging lens.
Explanation:
When an object is placed 25cm from Gbenga's eye, the glasses lens must produce an image 61cm away (Gbenga's eye near point).
An image 61cm from the eye will be (61cm - 1.6cm) from the glasses.
i.e. [tex]d_{i}=61cm-1.6cm=59.4cm[/tex]
and [tex]d_{o} = 25cm - 1.6cm = 23.4cm[/tex]
note [tex]d_{i}[/tex] will be negative because the image is formed on the same side as the object.
finally, [tex]d_{i}=-59.4cm\\d_{o}=23.4cm[/tex]
the formula for finding the focal length [tex]f[/tex] is given as
[tex]f=\frac{d_{i}d_{o} }{d_{o}+d_{i} }[/tex]
[tex]f=\frac{-59.4*23.4}{23.4-59.4} \\[/tex]
[tex]f=\frac{-1389.96}{-36}[/tex]
[tex]f=38.61cm[/tex]
The focal length is positive which indicates converging lens
power [tex]p=\frac{1}{f}[/tex]
but [tex]f\\[/tex] must be in metres
Therefore, [tex]f=38.61cm=0.3861m[/tex]
[tex]p=\frac{1}{0.3861}[/tex]
[tex]p=2.59 Diopter[/tex]
