# Lenses and Geometrical Optics

## Section Overview:

The action of a simple lens, similar to many of those used in the microscope, is governed by the principles of refraction and reflection and can be understood with the aid of a few simple rules about the geometry involved in tracing light rays through the lens. The basic concepts explored in this discussion, which are derived from the science of Geometrical Optics, will lead to an understanding of the magnification process, the properties of real and virtual images, and lens aberrations or defects.

### Review Articles

• #### Introduction to Lenses & Geometrical Optics

Lens is the common name given to a component of glass or transparent plastic material is designed to produce either a convergence or divergence of light passing through the material.

• #### Common Aberrations in Lens Systems

Microscopes and other optical instruments are commonly plagued by lens errors that distort the image by a variety of mechanisms associated with defects resulting from the spherical geometry of lens surfaces.

### Lens Interactive Tutorials

• #### Simple Bi-Convex Thin Lenses

Analyze the relationship and see how changes to the focal length and object size affect the size and position of the focused image formed by a simple thin lens in this interactive tutorial.

• #### Simple Magnification

Magnifying glasses produce a virtual image that is magnified and upright. This interactive tutorial demonstrates how a simple, thin bi-convex magnifying lens works to produce a magnified virtual image on the retina.

• #### Magnification with a Bi-Convex Lens

Single lenses capable of forming images are useful in tools designed for simple magnification applications, such as loupes, eyeglasses, single-lens, etc. See how a simple bi-convex lens can be used to magnify an image.

• #### Image Formation with Converging Lenses

Ray traces are utilized to show how images are formed by the primary types of converging lenses, and the relationship between the object and image formed by the lens as a function of distance between the object and focal points.

• #### Image Formation with Diverging Lenses

Ray traces are utilized to show how images are formed by the primary types of converging lenses, and the relationship between the object and image formed by the lens as a function of distance between the object and focal points.

• #### Geometrical Construction of Ray Diagrams

To represent a train of propagating light waves involves the application of geometrical optics determining size and location of images formed by a lens system. See how light rays can establish the parameters of an imaging scenario.

• #### Perfect Lens Characteristics

The simplest imaging element in an optical microscope is a perfect lens, which ideally is free of aberration and focuses light onto a single point. Explore how light waves propagate through and are focused by a perfect lens.

• #### Perfect Two-Lens System Characteristics

To represent a perfect lens as a system composed of two individual lens elements when a point source of light does not lie in the focal plane of a lens is common. Explore the off-axis oblique light rays passing through such a system.

• #### Radius and Refractive Index Effects on Lens Action

Analyze how variations in the refractive index and radius of a bi-convex lens affect the relationship between the object and the image produced by the lens.

### Optical Aberration Interactive Java Tutorials

• #### Astigmatism

Explore the relationship between astigmatism and comatic aberrations, and how astigmatism aberrations are manifested by the off-axis image of a specimen point appearing as a line or ellipse instead of a point.

• #### Chromatic Aberration

Learn more about chromatic aberrations and how when white light passes through a simple or complex lens system, the component wavelengths are refracted according to their frequency.

• #### Comatic Aberration

Learn about comatic aberrations and how they are mainly encountered with off-axis light fluxes and are most severe when the microscope is out of alignment, as well as the result of when these aberrations occur.

• #### Curvature of Field

Learn as this tutorial explains the curvature of field in optical microscopy and how it is a common and annoying aberration that is familiar to most experienced microscopists.

• #### Geometrical Distortion

Explore the two most prevalent types of distortion, positive and negative, and how they can often be present in very sharp images that are otherwise corrected for spherical, chromatic, comatic, and astigmatic aberrations.

• #### Spherical Aberration

Learn about the most serious of the monochromatic defects that occurs with microscope objectives, the spherical aberration, which causes the specimen image to appear hazy or blurred and slightly out of focus.

#### Contributing Authors

Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747.

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Matthew Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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