A dissecting microscope is designed to have a large distance...

A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is $5.0 \mathrm{~cm}$, the focal length of the eyepiece is $4.0 \mathrm{~cm}$, and the distance between the lenses is $32.0 \mathrm{~cm} .$ (a) What is the distance between the object and the objective lens? (b) What is the angular magnification?

A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is $5.0 \mathrm{~cm}$, the focal length of the eyepiece is $4.0 \mathrm{~cm}$, and the distance between the lenses is $32.0 \mathrm{~cm} .$
(a) What is the distance between the object and the objective lens? (b) What is the angular magnification?

Key Concepts

Thin Lens Equation

The thin lens equation, 1/f = 1/do + 1/di, describes the relationship among a lens's focal length (f), the object distance (do), and the image distance (di). This concept is pivotal for determining where an image forms relative to the lens and is fundamental in analyzing and designing optical instruments, including microscopes.

Compound Microscope Structure

A compound microscope consists of at least two lenses: an objective and an eyepiece. The objective lens first creates a real, magnified image of the specimen, which is then further magnified by the eyepiece to produce a final virtual image for the viewer. Understanding this two-stage image formation is essential for grasping how microscopes achieve high levels of magnification.

Angular Magnification

Angular magnification is the ratio of the angle subtended by the image when viewed through the optical instrument compared to the angle subtended by the object when viewed with the naked eye. In microscopes, the total angular magnification is generally the product of the magnifications provided by both the objective and the eyepiece, enabling even very small objects to be seen in great detail.

Tube Length and Working Distance

The tube length is the distance between the objective and eyepiece lenses in a microscope, and it largely determines where the intermediate image is formed. In instruments like a dissecting microscope, a long working distance (the distance between the object and the objective lens) is designed into the system to allow easier manipulation or observation of larger or three-dimensional objects.

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