The eyepiece of a microscope has a focal length of 1.25 cm and the objective lens focal length

step 1 In this problem, we have a microscope, and we have the information for the focal length of the o

The eyepiece of a microscope has a focal length of 1.25 cm...

The eyepiece of a microscope has a focal length of $1.25 \mathrm{~cm}$ and the objective lens focal length is $1.44 \mathrm{~cm}$. (a) If the tube length is $18.0 \mathrm{~cm}$, what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?

The eyepiece of a microscope has a focal length of $1.25 \mathrm{~cm}$ and the objective lens focal length is $1.44 \mathrm{~cm}$.
(a) If the tube length is $18.0 \mathrm{~cm}$, what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?

Key Concepts

Compound Microscope

A compound microscope is an optical instrument that uses two or more lenses to magnify small objects. It typically consists of an objective lens that forms a real, magnified image of the specimen and an eyepiece (ocular) lens that further magnifies this image for the viewer. Understanding its design is essential as it ties together how multiple lens systems work in sequence to offer high levels of magnification.

Angular Magnification

Angular magnification refers to the ratio of the angle subtended by the image at the observer's eye to the angle subtended by the object when viewed with the naked eye. In devices like microscopes, it is the cumulative effect of the magnifications provided by both the objective and the eyepiece, determining how large the specimen appears to the viewer. It is a central concept for evaluating and comparing the performance of optical instruments.

Objective Lens

The objective lens is the first optical element in a compound microscope that is closest to the specimen. Its primary role is to collect light from the object and produce a real, magnified image that serves as the object for the eyepiece. The focal length of the objective lens is a critical parameter, as it directly affects both the overall magnification and the resolution of the microscope.

Eyepiece

The eyepiece, or ocular lens, is the lens through which the observer views the magnified image produced by the objective lens. It serves to further enlarge the real image into a virtual image that can be comfortably and clearly observed by the human eye. The focal length of the eyepiece influences its angular magnification and plays a key role in the final magnification provided by the microscope.

Tube Length

Tube length in a microscope is the distance between the objective and eyepiece lenses, typically measured from the back focal plane of the objective to the front focal plane of the eyepiece. This length is significant because it determines the position of the intermediate, real image formed by the objective lens, and thereby affects the overall magnification and optical performance of the microscope system.

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