Solve the Thin-Lens Equation: How & Why It Works

  • Thread starter twitch94301
  • Start date
In summary, the thin-lens equation states that 1/distance from lens to object + 1/distance from lens to image = 1/focal length. This is based on the idea that a lens has a linear relationship between the distance a ray passes through off axis, and the amount the ray is kinked on passing through. By considering the angle of the ray from the object and the image, the formula can be derived.
  • #1
twitch94301
2
0
Hey. I understand the thin-lens equation and that it is 1/distance from lens to object + 1/distance from lens to image = 1/focal length. But, I was wondering how/why it works. If someone knows, I would appreciate the help. Thanks.
 
Science news on Phys.org
  • #2
The idea of a lens is to have a linear relationship between the distance a ray passes through off axis, and the amount the ray is kinked on passing through. Let us call the former quantity [itex]r[/itex] and the latter [itex]\Delta\theta[/itex]. The proportionality constant is [itex]f[/itex], the focal length. So we have
[tex]r=f\Delta\theta[/tex]
If a ray comes from a point on axis a distance [itex]o[/itex] upstream of the lens, and if [itex]\theta_o[/itex] is the angle, then for small angles, [itex]\theta_o=r/o[/itex].
If this ray comes to a point on axis a distance [itex]i[/itex] downstream of the lens, and if [itex]\theta_i[/itex] is the angle, then for small angles, [itex]\theta_i=r/i[/itex].
Now, realize that
[tex]\Delta\theta=\theta_o+\theta_i[/tex]
and you have your formula.
 
  • #3
Thanks for the help.
 

1. What is the Thin-Lens Equation and why is it important?

The Thin-Lens Equation is a mathematical formula that relates the focal length, object distance, and image distance of a thin lens. It is important because it allows us to calculate the image position and size formed by a lens, which is crucial in understanding how optical systems like cameras and microscopes work.

2. How is the Thin-Lens Equation derived?

The Thin-Lens Equation is derived using the principles of geometric optics and the laws of refraction and similar triangles. By drawing ray diagrams and using the properties of light, we can come up with the formula that relates the distance of the object, image, and the focal length of the lens.

3. What are the assumptions made in the Thin-Lens Equation?

The Thin-Lens Equation assumes that the lens is thin, meaning its thickness is negligible compared to its other dimensions. It also assumes that the lens has a spherical shape and that light rays passing through the lens are not significantly bent or aberrated.

4. Can the Thin-Lens Equation be used for all types of lenses?

No, the Thin-Lens Equation is only applicable for thin lenses, which have a thickness much smaller than their focal length. This includes lenses such as convex and concave lenses, but not thick lenses, like a magnifying glass or a microscope objective.

5. How is the Thin-Lens Equation used in real-life applications?

The Thin-Lens Equation is used in a variety of real-life applications, including camera lenses, eyeglasses, and telescopes. It allows us to predict and control the location and size of the image formed by a lens, making it an essential tool in optics and imaging technology.

Similar threads

Replies
10
Views
1K
  • Optics
Replies
5
Views
1K
  • Optics
Replies
10
Views
779
Replies
1
Views
1K
Replies
10
Views
344
Replies
8
Views
2K
  • Optics
Replies
3
Views
900
Replies
3
Views
812
  • Optics
Replies
1
Views
1K
Back
Top