Geometrical Optics: Explaining 2 Focus Positions

[jst81161]

Homework Statement

Explain why for a given object screen distance there are two positions where the image is in focus. Is this always true?

Homework Equations

The Attempt at a Solution

 

[berkeman]

Two positions of what, the lens? What kind of lens? What is the background for this question? What are the relevant equations?

 

[m2003]

Geometrical optics explains the behavior of light as it travels through different mediums and interacts with objects. When light rays pass through a lens, they undergo refraction, which causes them to converge or diverge depending on the shape of the lens. In the context of this question, we are considering a lens with a fixed distance between the object and the lens, known as the object screen distance.

According to the thin lens equation, 1/f = 1/s + 1/s', where f is the focal length of the lens, s is the distance between the object and the lens, and s' is the distance between the lens and the image. This equation shows that for a given object screen distance, there are two possible positions for the image to be in focus, known as the two focus positions.

The first focus position occurs when the object is placed at a distance equal to the focal length of the lens (s = f). In this case, the light rays from the object are refracted by the lens and converge to a point on the other side, creating a clear and focused image. This is known as the principal focus.

The second focus position occurs when the object is placed at a distance greater than the focal length of the lens (s > f). In this case, the light rays are still refracted by the lens, but they converge at a point on the same side as the object, creating a magnified and inverted image. This is known as the virtual focus.

Therefore, for a given object screen distance, there are two focus positions because of the nature of refraction and the properties of lenses. However, this is not always true. If the object is placed at a distance less than the focal length of the lens (s < f), the light rays will diverge after passing through the lens, and no real image will be formed. This is known as the diverging position and does not result in a focused image.

In conclusion, the existence of two focus positions for a given object screen distance is a result of the fundamental principles of refraction and the characteristics of lenses. However, it is not always true and depends on the specific conditions of the object and lens system.