Draw ray diagrams to show how a convex lens can produce (a) a real image that is smaller than th

Draw ray diagrams to show how a convex lens can produce (a)...

Key Concepts

Ray Diagrams

Ray diagrams are schematic representations used in geometrical optics to illustrate the paths taken by light rays as they pass through optical devices like lenses and mirrors. They provide a visual tool to determine the location, size, orientation, and type (real or virtual) of the images formed, aiding in the conceptual understanding of how optical systems function.

Magnification

Magnification in optics is the measure of how much larger or smaller an image is compared to the object, and it is calculated by the ratio of the image distance to the object distance. In a convex lens system, the magnification determines if a real image is larger or smaller than the object depending on the object’s placement relative to the focal length. This concept plays an important role in designing optical devices where maintaining the desired image size is critical.

Virtual Image Formation

A virtual image occurs when the diverging light rays appear to originate from a point behind the lens, even though they do not actually converge there. In a convex lens, if an object is placed within the focal length, the rays after refracting diverge, and an observer perceives them as coming from an image that is erect and magnified. Virtual images cannot be projected on a screen, as they exist only by perception.

Convex Lens

A convex lens, also known as a converging lens, is a transparent optical device with at least one curved surface that causes incoming parallel light rays to converge to a focal point. Its behavior under the lens-maker's equation enables it to form images by bending light, making it essential for applications ranging from magnifying glasses to corrective eyewear and cameras.

Real Image Formation

A real image is formed when light rays converge at a point after passing through a lens or reflecting off a mirror. In the case of a convex lens, when the object is placed outside the focal length, the lens converges the rays to produce an image that can be projected onto a screen. This image can be inverted and its size relative to the object depends on the object’s distance from the lens, resulting in images that are either larger or smaller than the object.

Transcript

00:01 In this problem, we're asked to draw a diagram to show where a real image is produced that is smaller than the height of the object, where a real image is produced, where the height is greater than the height of the object, and where a virtual image is produced.

00:15 And that's going to happen at these three positions, at position one, position two, and position three.

00:21 So at position one, you're going to have an object, which i'm going to represent by an arrow.

00:28 And to draw your ray diagram, you're going to draw a parallel line until you hit your lens, and then you're going to go through your focal point.

00:43 And this works best with a ruler.

00:45 Your second line is going to go through the center of that lens.

00:53 Now where the two lines intersect, that is where you have your image.

00:58 You can see how it is inverted.

01:00 Inverted images are real images.

01:04 And you can see how this is the height of the object and this is the height of the image.

01:12 You can see it's just a smidge bigger.

01:14 Actually, if we were to move it further back, that image would be, actually, that image would be a little bit smaller.

01:22 And so then we can look at position two.

01:25 Now that we've gotten a little bit closer, so this dot right here, this represents the focal.

01:30 Now that we've gotten a little bit closer, we're going to redraw those lines, again, parallel to the point.

01:35 To the principal axis, and then we're gonna go through the focal...

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