A converging lens has focal length 4.8 cm . A 1.5-cm-high arrow is located 11 cm from the lens

A converging lens has focal length 4.8 cm . A 1.5-cm-high...

Key Concepts

Converging Lens

A converging lens is a type of lens that causes incoming parallel rays of light to converge at a point known as the focal point. It is characterized by its ability to produce real, inverted images when the object is placed beyond the focal length, and it is a central element in geometrical optics for understanding image formation.

Focal Length

The focal length of a lens is the distance from the center of the lens to the point where parallel rays of light converge after refraction. It is a key parameter that affects how strongly a lens can bend light, influencing both the size and position of the image formed.

Thin Lens Equation

The thin lens equation, given by 1/f = 1/d_o + 1/d_i, is a fundamental relation in optics that links the object distance, image distance, and focal length of a lens. It is used to calculate the position and distance of the image relative to the lens and forms the theoretical basis for predicting image formation.

Ray Tracing Method

Ray tracing is a graphical technique used to determine the position, orientation, and size of the image produced by an optical system. By drawing key rays—such as those parallel to the principal axis, through the focal point, and through the center of the lens—the approximate location and properties of the image can be determined accurately on a full-scale diagram.

Magnification

Magnification is the ratio of the image size to the object size and indicates how much larger or smaller the image is compared to the original object. It is calculated using the distances from the lens, and its sign denotes the orientation of the image (inverted or upright), providing insights into the overall characteristics of the imaging process.

Transcript

00:02 In problem 46, a converging lens has a focal length of 4 .8 centimeters.

00:07 A 1 .5 centimeter high arrow is located 11 centimeters from the lens with the lowest point 4 millimeters above the lens axis.

00:16 Make a full -scale ray tracing diagram to locate both ends of the image and confirm using the lens equation.

00:23 So i'm going to do both.

00:24 It's hard to do a full to scale ray tracing diagram without rulers and a scaled.

00:32 System and i don't have that here on this whiteboard, but i can draw the ray diagram and then we can use the lens equation to see if our answers make sense.

00:42 So our focal length is 4 .8.

00:44 We know the height of the image is, i'm sorry, the height of the object is 1 .5 centimeters, but it's 11 centimeters, so the object distance is 11 centimeters from the lens, but it's 4 millimeters above the lens axis.

01:00 So that's just, that's not really a thing that normally has its own designated value.

01:06 This is four millimeters.

01:07 So i'm going to put that in centimeters.

01:09 That's 0 .4 centimeters.

01:11 So if the object is 1 .5 centimeters high, i'm looking for a point that's 1 .9 centimeters above the surface.

01:21 Or, sorry, above the principal axis.

01:23 So let's just draw the rays in.

01:26 It's hard to draw straight lines here, at least consistently.

01:32 Whoa, there we go.

01:34 And then there's that one.

01:38 In parallel goes out through the focal point.

01:41 In through the focal point comes out parallel.