Why Are Both X- and Y-Intercepts Equal to 1/f in the Lens' Equation?

[jaejoon89]

For the Lens' equation

1/f = 1/u + 1/v

why can both the x- and y-intercepts be considered equal to 1/f?

 

[Dadface]

When u becomes infinite what does 1/u become?What happens when v becomes infinite?

 

[nlightner]

The Lens' equation is a fundamental equation in optics that describes the relationship between the focal length (f) of a lens, the object distance (u), and the image distance (v). In this equation, the x-intercept represents the object distance (u) and the y-intercept represents the image distance (v).

Now, for both the x- and y-intercepts to be equal to 1/f, it means that the object distance (u) and the image distance (v) are both equal to the focal length (f). This is because when we plug in 1/f for both u and v in the equation, it simplifies to:

1/f = 1/1/f + 1/1/f
1/f = 2/f
1 = 2

This is only possible if both u and v are equal to f. In other words, the object is placed at a distance of f from the lens, and the image is formed at a distance of f from the lens. This is known as the "principle of conjugate foci."

In summary, both the x- and y-intercepts can be considered equal to 1/f because they represent the object and image distances, respectively, and when both are equal to 1/f, the equation simplifies and follows the principle of conjugate foci. This highlights the importance of the focal length in determining the properties of an optical system.