ENE 492

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## ENE 492

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**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?