In a compound microscope, the focal length of the objective...

In a compound microscope, the focal length of the objective is $3.50 \mathrm{~cm}$ and that of the eyepiece is $6.50 \mathrm{~cm}$. The distance between the lenses is $26.0 \mathrm{~cm} . \quad$ (a) What is the angular magnification of the $\mathrm{mi}-$ croscope if the person using it has a near point of $35.0 \mathrm{~cm} ? \quad$ (b) If, as usual, the first image lies just inside the focal point of the eyepiece (see Figure 26.32), how far is the object from the objective? (c) What is the magnification (not the angular magnification) of the objective?

Key Concepts

Compound Microscope

A compound microscope is an optical instrument that uses two or more lenses to produce a magnified image of a small object. It typically consists of an objective lens, which gathers light from the specimen and produces a real, inverted image, and an eyepiece lens, which magnifies this intermediate image to create a final, enlarged virtual image for the observer.

Angular Magnification

Angular magnification refers to the ratio of the angle subtended by the final image, as seen through the optical instrument, to the angle subtended by the object when viewed directly with the naked eye. This measure is crucial in devices like microscopes and telescopes, where the goal is to enhance the perceived size of distant or very small objects.

Focal Length

The focal length of a lens is the distance from the lens to the point where parallel rays of light converge (or appear to diverge from, in the case of a diverging lens). It is a key parameter that determines the magnifying power and the image formation characteristics of an optical system.

Near Point (Least Distance of Distinct Vision)

The near point, or least distance of distinct vision, is the closest distance at which the eye can comfortably focus on an object. In microscope design, this distance often defines the image location for maximum angular magnification, influencing how the optical system is configured for comfortable viewing.

Objective Lens Magnification

The magnification provided by the objective lens is determined by the ratio of the intermediate image distance and the object distance, based on the lens formula. This magnification is critical as it sets the initial scale of the image, which is later further increased by the eyepiece.

Lens Separation and Image Formation

The separation between the objective and eyepiece lenses in a compound microscope affects the position and nature of the intermediate image formed by the objective lens. Proper spacing ensures that the intermediate image is located at the optimal position relative to the eyepiece’s focal point, which is key to achieving the desired overall magnification and image clarity.

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