Optics

Optics

Real Images and the Thin Lens Equation

Description:

            This investigation explores the formation of real images, images formed by converging light, with convex lenses. This lab allows us to explore the phenomena of real images by projecting images in various configurations. The lab then introduces the mathematical relationships governing the phenomena that help back up our observations of the variables that affect the formation of a real image.

Purpose:

           The objectives for this lab are to use convex lenses to produce real images, observe the characteristics (appearance, orientation, magnification) of real images, and explore the mathematical relationship between object distance, image distance, and focal length in real images.

Figure 1: Set up

Results:

             5)
Graph 1: Image distance vs. distance to object


7)
                 a) As object distance increases, the image distance decreases.
                 b) No, the graph does not appear to be linear.
          9)
Graph 2: 1/di vs. 1/do and equation of graph

         10) The correlation value of the graph of the inverse is -0.999791. Since this number is extremely close to one, it indicates a good linear fit.
         11) The y-intercept (b) of this equation is 0.09959 which is approximately equal to 0.1. The significance of this value is that 0.1 is equal to 1/10, implying that the y-intercept is the inverse of the lens's focal length and that its units are 1/cm.

Equations / Calculations:

      Thin lens equation that shows the relationship between object distance (do) and image distance (di):
                1/f = 1/do + 1/di
      This equation explains why we found a linear relationship between 1/do and 1/di and why the image distance decreased when we increased the distance between the object and the lens.

Analysis:

              1) Using the thin lens equation, we predicted that, if we were to place the light source 33cm from the lens, an image would appear at 14.37cm.
              2) Using the thin lens equation, the image distance for a lens with a 20cm focal length and an object placed at 33cm would be 50.77cm.
              3) Using the thin lens equation, the y-intercept of a graph with a 15cm focal length would be 1/15cm.
              4) If the light source were positioned 33cm from a lens with a 15cm focal length, the screen should be placed at 27.5 cm.