Question

Chapter 10 Lenses Learning Objectives During this lab, you will, use the Law of Sagitta to determine the radius of curvature of a lens use the lens equation to determine focal length, . use the lensmaker's formula to determine the index of refraction of a trans- parent material. 10.1 Pre-lab This pre-lab will introduce you to a concept in geometrical optics known as ray tracing. Given an object that emits or reflects light, you can place a lens in the path of some of the light from that object. Some of the light will pass through the lens. As you know, light that passes from a medium with one index of refraction (such as air) to another (such as glass) is refracted. A ray trace diagram is a sketch that shows what happens to certain key rays of light as they travel from the object through the lens and beyond Most objects that emit or reflect light will emit or reflect it in all directions (uni- formly). It would be tedious to sketch so many light rays, and besides, you can never sketch 'all' of them, any more than you can draw all the electric field lines around a charged particle. They are merely a useful concept, not a physical phe- nomenon. To keep things simple, ray trace diagrams often involve only 3 key rays, called the "principle rays Light can be conceptualized either as a series of tays that travel in straight lines, or as a series of "wavelets", often sketched as ripples, that travel away from the source. In this case, it happens that the ray model is more convenient CHAPTER 10. LENSES [10.1] Action-Item: Download and run the PhET simulation "Geometric Optics". You should see a sketch of an object, a thin, convex lens, and an image, with two light rays passing from one particular point on the object through the lens, to one particular point on the image, and beyond. The horizontal line stretching across the screen is called the principle axis. The small "x marks are the focal points of the lens. Familiarize yourself with the controls. Once you are ready, switch from "Marginal rays" to "Principle rays Move the object forward, backward, and side-to-side. The principle rays and image should also move. 10.2] Question: Use the simulation to answer the following questions: a. What happens to the image as you increase the distance between the b. Describe what happens as you move the object inside the focal point on c. Move the object until the object is slightly larger than the image, and object and the lens? the object side of the lens along the principle axis you can see all three principle rays. Increase the 'curvature radius'. What happens to the lens? What happens to the image? Restore the curvature radius to a value around 0.8 m. Increase the 're fractive index'. What happens to the principle rays? What happens to the image? d. [10.3] Question: Using this simulation, describe each principle ray. Your goal is to describe each ray in words in a way that allows someone else, who has not seen the diagram but who has read your verbal description, to sketch each principle ray correctly from your description. Include your description and a sketch that allows your TA to identify each ray visually in your an- swer (for example, you could number the rays and provide a description by number). You may find the "2nd point from the simulation to be a useful reference. L [10.4] Question: Continue working with the simulation until you are confi- dent that you understand the properties that affect a lens's ability to image an object. What affects the size of the image? What affects the brightness? What affects the position of the image? List the properties you discovered in your answer 10.2 Introduction This week, you will use lenses and light sources to explore some basic principles of geometric optics. In the end, you will determine the index of refraction of an unknown transparent material. 2 Laboratory Manual

Answer 1

10.2

a) As the object gets far from the lens, the image becomes smaller and moves towards the lens.

b) The refracted rays diverge as the object moves inside the focal point of the lens. They converge on the object side of the lens and create a bigger virtual image.

c) The lens becomes thinner as the radius of curvature is increased. The image moves further from the lens and gets bigger as the radius of curvature is increased.

d) As the refractive index is increased the principle rays bend closer to the axis of the lens. The image comes closer to the lens and turns smaller.

10.3

Principle ray descriptions:

The principle ray that goes through the lens and parallel to the principle axis goes through the focal point after refraction.

The principle ray that goes through the focal point on the object side of the lens and through the lens refracts out as a parallel ray to the principle axis.

The principle ray that goes through the central point if the lens remains straight after refraction.

10.4

Size of the image is affected by the distance between the lens and the object, refractive index and radius of curvature. If the object is outside of focal point, more the distance, smaller the image. Inside the focal point, more distance means bigger object. Increasing radius of curvature increases image distance, increasing refractive index decreases the distance between the lens and the image.

Brightness of the image is also affected by the distance between the lens and the object, and the size of the lens. More the distance, dimmer the image. Larger the lens brighter the object.

Position of the image is entirely dependent on the object's position. If the object is outside the focal point (object side) the image is going to be on the other side. If the object is inside the focal point of the lens the image is going to be virtual, and on the same side as the object.