at what distance would a convex magnifing lens that has a focal length of 10 cm have to be held for an image to appear upright and 3 cm tall?
[6.67cm]
To find the distance at which a convex magnifying lens needs to be held for an upright image of a certain height, you can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance from the lens
- u is the object distance from the lens
In this case, the focal length (f) is given as 10 cm, and the image height (h) is given as 3 cm. We need to find the image distance (v).
Since the question mentions that the image is upright, we know that the image distance is positive (+v).
Now, let's solve for v using the lens formula:
1/10 = 1/v - 1/u
Since the object distance (u) is not given, we can assume it to be large for a magnifying lens. For simplicity, we can take it as infinity (∞). This is a reasonable approximation for a magnifying lens since the object is usually placed farther away.
1/10 = 1/v - 1/∞
As 1/∞ approaches zero, the equation simplifies to:
1/10 = 1/v
Now, rearrange the equation to solve for v:
v = 10 cm
Therefore, the image distance (v) is equal to 10 cm. This means the lens needs to be held at a distance of 10 cm from the object for the image to appear upright and 3 cm tall.