ENE 492 Fundamental of Optical Engineering Lecture 2
Converging lens • In order to locate the image, the 2 rays are needed as • The parallel ray: parallel to the axis and then, after refraction, passes through another focal point. • The focal ray: passes through a first focal point then, after refraction, is parallel to the axis. • The chief ray goes through the center of the lens without deviation since the lens is thin.
Derivation of Gauss’ Thin Lens Equation • L.H.S. • R.H.S.
Derivation of Gauss’ Thin Lens Equation • Take ratio (1) = (2), we have
Derivation of Gauss’ Thin Lens Equation • Multiply both sides by 1/ss’f, this yields • Finally, we have
Derivation of Gauss’ Thin Lens Equation • Magnification, • From (2) • From (3) x s’
Derivation of Gauss’ Thin Lens Equation • So that,
Conventions for lenses • Light travels from left to right. • All distances are measured from the plane of a lens. • Object to the left of a lens is called object distance s, and s is negative. • The image distance s’ could be positive (real image) and negative (virtual image).
Conventions for lenses • The focal length, f • f is ‘+’ for converging lens. • f is ‘-’ for diverging lens. • y’ is the height of an image. • y’ is ‘+’ for upright image. • y’ is ‘-’ for inverted image. • Magnification M • M is ‘+’ for upright image. • M is ‘-’ for inverted image.
Example • Find s’ and M for these cases of object distances.
Off-axis rays • In case of off-axis rays incident on a converging lens, the displacement of spot in focal plane can be found as
Off-axis rays • d = ftanθ • If θ is small, then tan θ θ. • d fθ……Displacement of spot in focal plane.
Diverging Lens • In case of diverging lens, focal length is negative in GTLE. • That leads an image distance to be ‘-’. • This means we always have a virtual image to the left of the lens.
Example • For diverging lens, find s’ and M for various s.
Lens combinations • We may use the combinations of lenses to form desired images.
Example • When an object is placed 75 mm in front of a converging lens, its image is 3 times as far away from the lens as when the object is at infinity. What is the focal length of the lens?