A microscope has an eyepiece that gives an angular...

A microscope has an eyepiece that gives an angular magnification of $5.00$ for a final image at infinity and an objective lens of focal length $15.0 \mathrm{~mm}$. The tube length of the microscope is $16.0 \mathrm{~cm}$. (a) What is the transverse magnification due to the objective lens alone? (b) What is the angular magnification due to the microscope? (c) How far from the objective should the object be placed?

Key Concepts

Focal Length

Focal length is a fundamental optical property of a lens that indicates the distance at which light rays initially parallel to the principal axis converge (or appear to diverge from) after passing through the lens. In microscopes, the focal lengths of the objective and eyepiece play a crucial role in determining both the magnification and the distance parameters for clear image formation.

Eyepiece Lens

The eyepiece lens in a microscope acts as a simple magnifier that further enlarges the real image produced by the objective lens. By taking the intermediate image and presenting it to the observer as if it were at infinity, it contributes to the overall angular magnification of the microscope.

Tube Length

Tube length in a microscope is the fixed distance between the objective lens and the eyepiece. It is an essential design parameter because it sets the distance at which the real image from the objective lens is formed before being further magnified by the eyepiece. The tube length affects the intermediate image position and, consequently, the overall magnification and image quality.

Transverse Magnification

Transverse magnification, sometimes referred to as lateral or linear magnification, is the ratio between the size of the image and the size of the object. In the context of microscopes, it typically describes how much larger the intermediate real image produced by the objective lens is relative to the actual object, and is determined by the distances involved in image formation.

Objective Lens

The objective lens is the primary lens in a microscope that is closest to the object being observed. It produces a real, magnified intermediate image of the specimen. Its optical characteristics, such as focal length and numerical aperture, are critical in determining the resolving power and overall magnification of the microscope.

Angular Magnification

Angular magnification is the ratio of the angle subtended by the image as seen by the eye to the angle subtended by the object at the unaided eye. In optical instruments such as microscopes and telescopes, it determines how much larger (in angular terms) the image appears compared to the object, which is particularly important when viewing objects too small or distant for the naked eye to resolve in detail.

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