Optics - Thin Lens Equation

Question 1

lens

Answer 1

• Lenses intercept some of the rays diverging from an object, and bend them so they converge to focus at an Image point. Of the many rays that hit the lens, a few of them are fairly easy to draw on a diagram. By seeing where those rays cross, we can see visually why they form an image at a particular distance. This process of drawing a few representative rays to see where the image forms is called “Ray Tracing,” and the pictures are called “Ray Diagrams.”
• Although in this course you will not be asked to provide your own ray diagram, it is important that you understand how it is done. The video lecture provides valuable information that will help you to understand how to do this.
• So lets say we have an object O at a distance do from a lens of focal length f. We are going to draw three special rays coming off the top of the object, and see where they cross; that is where the image forms. There are four special points we will use to draw the rays: The tip of the object O, the first focal point F1, the center of the lens C, and the second focal point F2.
• Ray 1: The first ray we draw leaves the tip of O and hits the lens at its center C. Because the lens is symmetric about that point, the ray comes out at the exact same angle at which it came in. In other words, the ray passes straight through the (thin) lens without getting bent.
• Ray 2: The second ray leaves the tip of O and passes through the first focal point, F1. When it hits the lens, it bends up, and comes out parallel to the axis.
• Ray 3: The third ray we’ll draw leaves O parallel to the axis. When it hits the lens, it bends, and goes where all parallel rays go: through the second focal point F2.
• When you draw all three rays, you find that they all cross at the certain point on the other side of the lens. That is where the Image of the object’s tip forms. The distance from that point to the lens is the image distance, di.
• If you drew this nicely, you could measure di off the diagram instead of calculating it. In practice, this is a nice way to double check your math: draw a quick ray diagram, and see if the picture agrees with the calculation.