A cub scout makes a simple microscope by placing two converging lenses of +18 D at opposite ends

A cub scout makes a simple microscope by placing two...

Key Concepts

Object Placement Relative to the Lens

Accurate placement of an object relative to a lens, especially the objective lens in a microscope, is necessary to ensure that a clear and adequately magnified image is obtained. This involves positioning the object at an appropriate distance such that it lies within the lens’s effective range for focusing light and forming a real image, making the design and adjustment of the microscope’s working distances an important aspect of its overall functionality.

Converging Lenses

Converging lenses, often referred to as convex lenses, are used to focus light and form images. Their behavior is characterized by a positive focal length and they are fundamental components in many optical instruments because they can converge parallel rays of light to a point, making them ideal for image formation in devices like microscopes, telescopes, and cameras.

Diopter and Focal Length Relationship

The diopter is a unit that quantifies the optical power of a lens and is defined as the reciprocal of the focal length expressed in meters. This relationship is crucial in designing optical devices, as it provides a direct way to calculate the focal length of a lens when its power in diopters is known, thereby guiding the arrangement and spacing of optical components in instruments.

Microscope Components

A simple microscope typically consists of two key lenses: an objective lens and an eyepiece. The objective lens gathers light from an object and creates a real, magnified image, while the eyepiece further magnifies this image for the viewer. The overall design, including the tube length which separates these lenses, is critical in determining the quality and degree of magnification achieved in the microscope.

Angular Magnification

Angular magnification describes the ability of an optical instrument to increase the apparent angular size of an object. In microscopes and other viewing devices, it is defined as the ratio of the angle subtended by the image seen through the instrument to the angle subtended by the object when observed directly. This concept is central to evaluating and designing instruments where human perception is based on angular size rather than linear dimensions.

Lens Formula and Image Formation

The lens formula, 1/f = 1/do + 1/di, establishes the relationship between the focal length (f) of a lens, the distance from the lens to the object (do), and the distance from the lens to the image (di). This equation is essential in predicting and controlling where an image will form, which is critical in the precise alignment of optical elements in a microscope or any other optical apparatus.

Transcript

00:01 In this problem, we have a microscope that is formed by two converging lenses.

00:08 So we call these lenses the objective and the ips.

00:13 And the problem says that the focal length of these lenses is 1 over 18, where 18 is the refracting power.

00:24 So remember that the focal length is just the inverse of the refractive power.

00:31 Also the problem says that the distance between these two lenses is 28 meters or 0 .28 meters.

00:39 And in the first part of the problem, we want to compute what is the tithe length.

00:45 So this l here.

00:47 So remember that in a microscope, this tithe length is just the distance between the two focal points of the lenses.

01:00 So this is the secondary focal point of the objective here, and this is the primary focal point of the ips.

01:10 So as we have the values of the focal length of the lenses and also this distance, we can easily compute l.

01:21 So l is just .28 minus 1 over 18, minus 1 .18 minus 1.

01:31 Over 18 from the figure and all of this is just 0 .17 mirrors.

01:42 In the second part of the problem we want to compute what is the angular, total angular magnification.

01:52 So remember that for a microscope this total angular magnification is minus l.

01:59 This l is the tube length over the focal length of the objective times the near distance over the focal length of the ips.

02:13 And remember that this near distance is 0 .25 meters...

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