A) Image position: -19.3 cm
B) Image height: 1.5 cm, upright
Explanation:
A)
In order to calculate the image position, we can use the lens equation:
![\frac{1}{p}+\frac{1}{q}=\frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bp%7D%2B%5Cfrac%7B1%7D%7Bq%7D%3D%5Cfrac%7B1%7D%7Bf%7D)
where
p is the distance of the object from the lens
q is the distance of the image from the lens
f is the focal length
In this problem, we have:
p = 13 cm (object distance)
f = 40 cm (focal length, positive for a converging lens)
So the image distance is
![\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{40}-\frac{1}{13}=-0.0519\\q=\frac{1}{-0.0519}=-19.3 cm](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bq%7D%3D%5Cfrac%7B1%7D%7Bf%7D-%5Cfrac%7B1%7D%7Bp%7D%3D%5Cfrac%7B1%7D%7B40%7D-%5Cfrac%7B1%7D%7B13%7D%3D-0.0519%5C%5Cq%3D%5Cfrac%7B1%7D%7B-0.0519%7D%3D-19.3%20cm)
The negative sign means that the image is virtual.
B)
In order to calculate the image height, we use the magnification equation:
![\frac{y'}{y}=-\frac{q}{p}](https://tex.z-dn.net/?f=%5Cfrac%7By%27%7D%7By%7D%3D-%5Cfrac%7Bq%7D%7Bp%7D)
where
y' is the image height
y is the object height
In this problem, we have:
y = 1.0 cm (object height)
p = 13 cm
q = -19.3 cm
Therefore, the image heigth is
![y'=-\frac{qy}{p}=-\frac{(-19.3)(1.0)}{13}=1.5 cm](https://tex.z-dn.net/?f=y%27%3D-%5Cfrac%7Bqy%7D%7Bp%7D%3D-%5Cfrac%7B%28-19.3%29%281.0%29%7D%7B13%7D%3D1.5%20cm)
And the positive sign means the image is upright.