We can use the thin lens formula to find the focal length of the lens:
1/f = 1/di + 1/do
where f is the focal length, di is the distance from the lens to the image, and do is the distance from the lens to the object. Since both the object and image are 16.0 cm from the lens, we can substitute do = di = 16.0 cm and solve for f:
1/f = 1/16.0 + 1/16.0
1/f = 1/8.0
f = 8.0 cm
So the focal length of the lens is 8.0 cm.
If the lens is moved so that it is 24 cm from the book, we can use the same formula to find the new distance to the image:
1/f = 1/di + 1/do
1/8.0 = 1/di + 1/24.0
1/di = 1/8.0 - 1/24.0
1/di = 1/12.0
di = 12.0 cm
So the distance from the lens to the new image is 12.0 cm.
To determine whether the new image will be magnified, reduced, or the same size compared to the original book, we can use the magnification formula:
m = -di/do
where m is the magnification. Since the image is inverted, we include a negative sign. We already know that do = 24.0 cm and di = 12.0 cm, so we can substitute these values and solve for m:
m = -di/do
m = -12.0/24.0
m = -0.5
Since the magnification is negative, the image is inverted. And since the magnification is less than 1 in absolute value, the image is reduced compared to the original book.