∙Figure 24.53 shows a small plant near a thin lens. The ray...

$\bullet$ Figure 24.53 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each syuare is 2.0 $\mathrm{cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use infor- mation from the diagram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where the image should be, and compare this result with the graphi- cal solution in part (c).

$\bullet$ Figure 24.53 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each syuare is 2.0 $\mathrm{cm}$ along the horizontal direction, but
the vertical direction is not to the same scale. Use infor- mation from the diagram to answer the following questions: (a) Using only the ray shown,
decide what type of lens (converging or diverging) this is.
(b) What is the focal length of the lens? (c) Locate the image
by drawing the other two principal rays. (d) Calculate where
the image should be, and compare this result with the graphi-
cal solution in part (c).

Key Concepts

Converging and Diverging Lenses

Converging lenses, also known as convex lenses, cause parallel incident light rays to converge at a focal point on the opposite side of the lens. Diverging lenses, or concave lenses, cause parallel rays to spread out as if they originated from a focal point on the same side as the object. Recognizing which type of lens is used is fundamental to understanding image formation and predicting the behavior of light rays.

Focal Length

The focal length of a lens is defined as the distance between the lens and its focal point, where initially parallel light rays converge (or appear to diverge from in the case of a diverging lens). The focal length is a crucial parameter that influences the image location and magnification, and is essential in the application of the lens equation.

Thin Lens Model

The thin lens model is a simplified representation used in geometric optics where the lens thickness is assumed to be negligible compared to the distances between the object, lens, and image. This approximation allows the application of simple formulas, such as the lens equation, and makes it easier to analyze the behavior of light rays through the lens.

Principal Rays

Principal rays are key rays drawn in ray diagrams to locate the image formed by a lens. They typically include the ray parallel to the optical axis (which refracts through the focal point), the ray passing through the center of the lens (which continues in a straight line), and the ray through the focal point (which refracts to emerge parallel to the optical axis). These rays help determine where the image forms and its characteristics.

Lens Equation and Image Formation

The lens equation, given by 1/f = 1/d_o + 1/d_i (where f is the focal length, d_o is the object distance, and d_i is the image distance), is a fundamental relation in geometric optics. This equation is used to calculate the position and size of the image formed by a lens, thereby linking the physical parameters of the lens with the optical properties of the system.

Transcript

00:01 All right, so this is similar to problem 54.

00:06 From the diagram, we see that the ray is bending away from the axis, away from optic axis, that is to say, by the lens.

00:21 And so this means that this means that this is a converging lens, or rather diverging, i should say, sorry.

00:31 Diverging lens.

00:32 Converging lens would be if the ray was bending toward the axis.

00:36 So diverging lens is what this is.

00:42 And for part b, we noticed that the ray that is shown actually intersects the optic axis on the left side of the lens.

00:58 And this would be one of the principal rays.

01:00 So this is one of the focus, so this point is a focus point and that is five squares, right? so each square is, each horizontal square is two centimeters.

01:11 So that would be 10 centimeters.

01:15 10 centimeters from the axis is where the focus point, or from the lens is where the focus point is.

01:23 And this is a diverging lens.

01:25 So focal length is negative 10 centimeters.

01:28 All right.

01:29 In part c, i show the principal ray diagram and you have the object all the way out here and its distance is 16 centimeters.

01:42 So we can count up the eight squares, eight times two is 16 from the diagram given in the book.

01:49 Focal length is 10 centimeters as we just found out.

01:52 So this is one of the foci...