Use a ruler to draw ray diagrams to locate the images of the following objects: (a) an object th

Use a ruler to draw ray diagrams to locate the images of the...

Key Concepts

Convex Lens

A convex lens, also known as a converging lens, is an optical device that bends incoming parallel rays towards a common point known as the focal point. It is widely used in image formation because it can produce either real or virtual images depending on the position of the object relative to its focal length.

Focal Length

The focal length is the distance between the center of a lens and its focal point, where parallel rays converge after passing through the lens. It is a crucial parameter in determining the nature and position of the image formed by the lens.

Lens Equation

The lens equation, commonly written as 1/f = 1/do + 1/di, relates the focal length (f) of the lens to the object distance (do) and the image distance (di). This equation is essential for quantitatively predicting where the image will form and whether it will be real or virtual.

Real and Virtual Images

Real images are formed when light rays converge at a point and can be projected onto a screen, while virtual images are formed when the rays appear to diverge from a common point. In ray diagrams, real images are typically inverted relative to the object, and virtual images are upright.

Magnification

Magnification refers to the ratio between the height of the image and the height of the object. It is determined by the distances of the object and the image from the lens. Magnification not only indicates the relative size but also whether the image is inverted or upright.

Ray Diagrams

Ray diagrams are graphical representations that use a few well-defined rays to locate the image formed by an optical system. In the context of lenses, key rays are drawn from the top of the object through the center of the lens, parallel to the principal axis, and towards the focal point, to determine the position, size, and orientation of the resultant image.

Transcript

00:01 So for this poem, you are going to need a ruler and preferably some graph paper.

00:05 So you're going to start off by drawing your lens.

00:08 And so i've drawn my lens right here in the middle.

00:11 And then i'm going to use an arrow as my object.

00:13 And i'm just going to choose some length for my arrow.

00:17 So let's say i make this about two centimeters tall.

00:21 Again, you do want to draw this to scale on your picture.

00:25 Since the focal length of your lens is 10 centimeters from my lens, my focal point is 10 centimeter from my lens, i can go ahead and mark off 30 centimeters, and that's where part a begins.

00:39 So when you're drawing your ray diagrams, your first ray is going to go parallel to the principal axis.

00:45 So your principal axis is this middle portion right here.

00:51 So you're going to draw your first ray parallel to the principal axis, and then once you hit that lens, you're going to go through your focal point on the other side.

01:00 So this focal point right here is 10 centimeters from the lens on the other side.

01:07 And then you're just going to go ahead and draw it straight through.

01:10 And then you're going to draw a second ray.

01:12 Again, starting from the top of your object, you're going to draw your line straight through the center of your lens and then draw it all the way through.

01:20 And where those two points intersect is where your image is going to be created.

01:24 So then you can fill in the rest of the diagram to draw in your image.

01:28 And you should be able to measure this distance.

01:32 This would be d .i for the first problem.

01:35 But we can also mathematically prove it as 1 over d .i plus 1 over d .o equals 1 over f.

01:45 1 over d .i equals 1 over f minus 1 over d .o.

01:50 And then 1 over my focal, which is 10, minus 1 over d .o, which is 30.

01:59 Get to a value of 0 .066 repeating.

02:07 Again, that's not my final answer.

02:09 I do need to inverse that.

02:10 So then, d .i.

02:11 Would be one over that value.