Aconverging lens has a focal length of 19.0 cm. locate the images for the following object distances. a) 41 cm b) 14cm

We can solve both parts of the problem by using the lens equation:

where
f is the focal length
is the distance of the object from the lens
is the distance of the image from the lens

Let's also keep in mind that for a converging lens, the focal length is taken as positive, so f=+19.0 cm.

(a) In this case, . So, the lens equation becomes

And so the distance of the image from the lens is

where the positive sign means the image is real, i.e. is located behind the lens (opposite side of the real object)

(b) In this case, . So, the lens equation becomes

And so the distance of the image from the lens is

where the negative sign means the image is virtual, i.e. is located in front of the lens (i.e. on the same side of the real object)