Calculating Focal Length and Image Height of a Lens

The image height is -2.55 mm, so it is inverted. In summary, a lens forms an image of an object 16 cm away from the lens, with the image being 12 cm away from the lens on the same side as the object. The focal length of the lens is -48 cm and the lens is diverging. The height of the image is -2.55 mm and it is inverted.
  • #1
fromthepast
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Homework Statement



A lens forms an image of an object. The object is 16 cm from the lens. The image is 12 cm
from the lens on the same side as the object. (a) What is the focal length of the lens? Is the
lens converging or diverging? (b) If the object is 8.5 mm tall, how tall is the image? Is it erect or inverted? Draw a principle-ray diagram.

Homework Equations



1/f = 1/s + 1/s'

The Attempt at a Solution



I got 6.8cm for the focal length and .638cm for the height. When I draw my principle-ray diagram, the object and image are to the left of the second focal point, which is to the left of the lens. Shouldn't the 2nd focal point be between the object and image on the left side of the lens?
 
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  • #2
Anybody?
 
  • #3
The image is at the same side as the object. Is the image real or virtual?

ehild
 
  • #4
virtual
 
  • #5
Your result for the focal length is not correct. The virtual image distance has minus sign in the lens formula. Calculate again.

ehild
 
  • #6
-48cm?
 
  • #7
Yes, the focal length is -48 cm. The lens is diverging so the focal length is negative.

ehild
 

Related to Calculating Focal Length and Image Height of a Lens

1. What is focal length and why is it important?

Focal length is the distance between the center of a lens and the point where light rays converge to form a sharp image. It is an important factor in determining the magnification and field of view of a lens.

2. How do I calculate the focal length of a lens?

The focal length of a lens can be calculated by measuring the distance between the lens and the image produced by an object at a known distance. This can be done using the lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

3. How do I calculate the image height of a lens?

The image height of a lens can be calculated using the magnification formula: M = -di/do, where M is the magnification, di is the image distance, and do is the object distance.

4. What is the difference between the focal length and the focal point of a lens?

The focal length of a lens is a physical measurement, while the focal point is a theoretical point where all light rays converge after passing through the lens. The focal point is located at a distance of one focal length from the lens.

5. How does changing the focal length affect the image produced by a lens?

Changing the focal length of a lens will alter the magnification and field of view of the image produced. A shorter focal length will result in a wider field of view and smaller magnification, while a longer focal length will result in a narrower field of view and larger magnification.

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