A microscope has an eyepiece of focal length 2.00 cm and an objective of focal length 3.00 cm .

A microscope has an eyepiece of focal length 2.00 cm and an...

A microscope has an eyepiece of focal length $2.00 \mathrm{cm}$ and an objective of focal length $3.00 \mathrm{cm} .$ The eyepiece produces a virtual image at the viewer's near point $(25.0 \mathrm{cm}$ from the eye). (a) How far from the eyepiece is the image formed by the objective? (b) If the lenses are $20.0 \mathrm{cm}$ apart, what is the distance from the objective lens to the object being viewed? (c) What is the angular magnification?

Key Concepts

Lens Equation

The lens equation 1/f = 1/do + 1/di is fundamental in geometric optics. It relates the focal length (f) of a lens to the distances of the object (do) and the image (di) from the lens. This concept allows one to determine how an image is formed by a lens, whether it is real or virtual, and is used in analyzing optical instruments like microscopes and telescopes.

Focal Length

Focal length represents the distance over which parallel rays of light are brought to a focus by a lens. In complex instruments, different lenses have different focal lengths which affect the formation and magnification of images. Knowing the focal length is essential for determining the position of both the object and image, and it plays a critical role in the overall design and function of optical systems.

Virtual Image

A virtual image is formed when light rays only appear to diverge from a point behind the lens rather than actually converging at that point. This concept is important in optical devices that are designed for comfortable viewing, such as eyepieces in microscopes, where the image is positioned at the near point of the eye to maximize clarity and ease of observation.

Compound Microscope

A compound microscope is an optical instrument that utilizes two lenses—the objective and the eyepiece—to produce a highly magnified image of a small object. The objective lens creates a real, inverted image that serves as the object for the eyepiece, which then magnifies this image further and forms a final virtual image that is easy for the observer to view.

Angular Magnification

Angular magnification refers to the ratio of the angle subtended by the image when viewed through an optical instrument to the angle subtended by the object when viewed directly. This concept is key in instruments such as microscopes and telescopes, where enhancing the apparent size of an object makes details clearer and more discernible to the human eye.

Transcript

00:02 In this problem we have a microscope with two lenses, two convergent lenses, and we have the value of the focal length of these two converging lenses.

00:15 So for the objective, we have the focal length here, and also for the ips.

00:23 The value is here.

00:26 And the problem says that the image that is produced by the ips is at the near point.

00:31 So the near point that is this point here is typically at 25 cerem mirrors from the lens.

00:41 So we can say that the image distance for the ips is 0 .25.

00:49 And as this image that is produced here for the ips is at the same side of the original object, this is a negative distance.

01:04 This is just a minus 0 .25 mirrors.

01:10 Okay, in the first part of the problem, we want to compute where is the distance between the object distance for the ips.

01:19 This is the distance from the image that is produced by the objective that then becomes the object for the ips and the ips.

01:29 So in order to get this value here, as we already have the image distance for the ips and the focal length for the ips, we can use just the lens equation for the ips.

01:44 So using that lens equation here, we'll just replace the value that we have here for the image distance and the focal length.

01:59 And replacing that numbers, this object distance for the ips is 0 .0185 meters.

02:12 So the object distance for the ips we can say that this value here is is a called it p is this number here so maybe at this point is the image that is produced by the objective.

02:34 Oh from here we can also get the image distance for the objective.

02:40 So for the objective, the image distance is all of this...

Please give Ace some feedback