A converging lens with a focal length of 19 cm is used to form an image on a screen that is 3.3 m to the right the lens. Where must the object be placed?
____m to the left of the lens?
Have you seen an equation that looks something like
1/Do + I/Df = 1/f ?
Well, you have now.
Di = image distance = 3.3 m
f = focal length = 0.19 m
Solve for Do (object distance) in meters
The object is close to the focal point. You have a highly magnified image
Okay, thanks!
You're welcome! Let me know if you have any other questions.
To find the position of the object, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the distance of the image from the lens, and
- u is the distance of the object from the lens.
Given:
focal length, f = 19 cm = 0.19 m
distance of the image, v = 3.3 m
We need to find the distance of the object, u.
Rearranging the lens formula, we get:
1/u = 1/f - 1/v
Substituting the values, we have:
1/u = 1/0.19 - 1/3.3
Calculating the right side of the equation:
1/u = 5.26316 - 0.30303
1/u = 4.96013
Now, we can find u by taking the reciprocal of both sides:
u = 1/4.96013
u ≈ 0.20143 m
Therefore, the object must be placed approximately 0.20143 m to the left of the lens to form an image on the screen that is 3.3 m to the right of the lens.