# Objective Magnification in Infinity Optical Systems

Infinity-corrected microscope optical systems are designed to enable the insertion of auxiliary devices, such as vertical illuminators and intermediate tubes, into the optical pathway between the objective and eyepieces without introducing spherical aberration, requiring focus corrections, or creating other image problems. In a finite optical system, light passing through the objective converges at the image plane to produce an image. The situation is quite different for infinity-corrected optical systems where the objective produces a flux of parallel light wavetrains imaged at infinity, which are brought into focus at the intermediate image plane by the tube lens. This tutorial explores how changes in tube lens and objective focal length affect the magnification power of the objective in infinity-corrected microscopes.

The tutorial initializes with the major optical train components (condenser, specimen, objective, tube lens, and eyepiece) of a virtual infinity-corrected microscope appearing in the window. A beam of semi-coherent light generated by the source passes through the condenser and is focused onto the specimen plane, subsequently being collected by the objective. The parallel flux of light rays exiting the objective are focused by the tube lens onto the intermediate image plane positioned at the fixed diaphragm of the eyepiece. The distance between the tube lens and the fixed eyepiece diaphragm is adjustable within a range of 160 and 200 millimeters using the **Reference Focal Length (L)** slider (equivalent to the **tube length** in older microscopes). In addition, the objective focal length can be varied from 2 to 40 millimeters by translating the **Objective Focal Length (F)** slider. As these sliders are translated, the individual components of the virtual microscope are readjusted to new positions.

To operate the tutorial, use the **Reference Focal Length** and **Objective Focal Length** sliders to alter the specifications of the virtual infinity optical system. The objective magnification (**M**) is calculated by dividing the reference focal length (**L**) of the tube lens by the objective focal length (**F**). As the critical focal length parameters of the microscope are varied, this calculation is automatically performed and the result is continuously updated and displayed in the space to the right of the objective drawing in the tutorial window. For example, a reference focal length of 180 millimeters and an objective focal length of 18 millimeters yield a magnification of 10x. The objective working distance is also presented graphically and updated as the microscope focal lengths are adjusted.

As previously listed, the basic optical components of an infinity system are the objective, tube lens, and the eyepieces. The specimen is located at the front focal plane of the objective, which gathers light transmitted through or reflected from the central portion of the specimen and produces a parallel bundle of rays projected along the optical axis of the microscope toward the tube lens. A portion of the light reaching the objective emanates from the periphery of the specimen, and enters the optical system at oblique angles, advancing diagonally (but still in parallel bundles) toward the tube lens. All of the light gathered by the tube lens is then focused at the intermediate image plane, and subsequently enlarged by the eyepiece.

In a finite optical system of fixed tube length, light passing through the objective is directed toward the intermediate image plane (located at the front focal plane of the eyepiece) and converges at that point, undergoing constructive and destructive interference to produce an image. The situation is quite different for infinity-corrected optical systems where the objective produces a flux of parallel light wavetrains imaged at infinity (often referred to as **infinity space**, and labeled in the tutorial window), which are brought into focus at the intermediate image plane by the tube lens. It should be noted that objectives designed for infinity-corrected microscopes are usually not interchangeable with those intended for a finite (160 or 170 millimeter) optical tube length microscope and vice versa. Infinity lenses suffer from enhanced spherical aberration when used on a finite microscope system due to lack of a tube lens. In some circumstances it is possible, however, to utilize finite objectives on infinity-corrected microscopes, but with some drawbacks. The numerical aperture of finite objectives is compromised when they are used with infinity systems, which leads to reduced resolution. Also, parfocality is lost between finite and infinity objectives when used in the same system. The working distance and magnification of finite objectives will also be decreased when they are used with a microscope having a tube lens.

The tube length in infinity-corrected microscopes is referred to as the **reference focal length** and ranges between 160 and 200 millimeters, depending upon the manufacturer. Correction for optical aberration in infinity systems is accomplished either through the tube lens or the objective(s). Residual lateral chromatic aberration in infinity objectives can be easily compensated by careful tube lens design, but some manufacturers choose to correct for spherical and chromatic aberrations in the objective lens itself. This is possible because of the development of proprietary new glass formulas that have extremely low dispersions. Other manufacturers utilize a combination of corrections in both the tube lens and objectives.