Optical microscopy uses optic principles to provide detailed images of samples. Antonie van Leeuwenhoek designed the first compound optical microscope in the 17th century to visualize blood cells, bacteria, and yeast cells. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes with enhanced magnification and resolution.
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...

Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...

The early pioneers of microscopy opened a window into the invisible world of microorganisms. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes that leveraged nonvisible light, such as fluorescence microscopy that uses an ultraviolet light source and electron microscopy that uses short-wavelength electron beams. These advances significantly improved magnification, image resolution, and contrast. By comparison, the...

The spirograph is a versatile tool for visualizing the relationship between geometry and mathematical representation. In particular, it demonstrates how polar coordinates offer an alternative framework for describing curves in comparison to Cartesian coordinates. Instead of specifying a point by its horizontal and vertical displacements (x, y), polar coordinates use a radius r, the distance from the origin, and an angle θ, measured counterclockwise from the polar axis. This system is...

The polar coordinate system provides a natural way to describe points in the plane when distances and directions are more meaningful than horizontal and vertical displacements. It is especially useful for modeling non-rectangular regions such as circles and spirals, where symmetry about a center point is easier to express than it is in a rectangular grid. A familiar example is a ship’s plan position indicator, which marks detected targets as dots positioned relative to the ship at the display’s...

The wavelengths of visible light ultimately limit the maximum theoretical resolution of images created by light microscopes. Most light microscopes can only magnify 1000X, and a few can magnify up to 1500X. Electrons, like electromagnetic radiation, can behave like waves, but with wavelengths of 0.005 nm, they produce significantly greater resolution up to 0.05 nm as compared to 500 nm for visible light. An electron microscope (EM) can create a sharp image that is magnified up to 2,000,000X.