A 5.0cm tall object is placed 16cm from a convex lens with a focal length of 8.4cm. What are the image height and orientation?
To determine the image height and orientation formed by a convex lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f represents the focal length of the lens,
- v represents the image distance from the lens, and
- u represents the object distance from the lens.
In this case, the object distance (u) is given as 16 cm, and the focal length (f) is given as 8.4 cm.
Let's plug these values into the lens formula:
1/8.4 = 1/v - 1/16
To solve for 'v', we need to simplify this equation. First, let's find the least common denominator by multiplying the equation through by 16v:
16v/8.4 = 16v/v - 16v/16
Simplifying further, we get:
1.9v = v - 16
Now, isolate 'v' on one side:
1.9v - v = -16
0.9v = -16
Divide both sides by 0.9:
v = -16 / 0.9
v ≈ -17.78 cm
Note: The negative sign indicates that the image is formed on the same side as the object (i.e., it's a virtual image).
Now, to determine the image height (h') and its orientation, we can use the magnification formula:
Magnification (m) = -v/u
Where:
- m represents the magnification of the lens.
Plugging in the values:
m = -(-17.78 cm) / 16 cm
m ≈ 1.11
Since the magnification (m) is positive, it indicates that the image is upright. The magnitude of the magnification (1.11) suggests that the image is slightly larger than the object.
Hence, the image height is slightly larger than the object's height, and the image is upright.