Question

I need help answering questions 1-6 please

Your group is working to develop and study new proteins. To analyze the composition of a protein mixture you have produced, the protein solution is placed in an electric field. Proteins with different total charges will drift at different speeds in the solution, and can be separated for further analysis.

Your group needs to focus an optical apparatus at known positions within the protein solution in order to record an image of a small part of the volume. For every point in an image, you must be able to specify the location of the corresponding point in the protein solution. For simplicity, you decide to model your optical apparatus with a single convex lens. Your group is investigating the relationships between the positions of points on an object and points in its image in two parts.

For this part, you investigate the relationship between a point of the object a distance from the principal axis and the distance of its corresponding point of the image from the principal axis.

1. Draw a fairly large sketch, showing a convex lens and a source of light (such as a vertical arrow). Label the lens's focal points, and position the source so that an image will be created, which could be projected on a screen.

2. Determine the position of the image, by sketching the paths of two light rays from the top of the light source. Indicate the position of the image in your sketch. Where should you position the screen in order to see the image?

3. To your initial diagram, add a second object at the same position, but approximately twice as long. Determine the position and size of the image, as you did for the first object. How do the position and size compare to those of the original object?

4. From your diagrams and geometrical knowledge of similar triangles, write an equation that relates the height of the object to the height of the image, in terms of the distance of the object from the lens and the distance of the image from the lens.

5. Write an equation for the linear magnification in terms of distance of the object from the lens and the distance of the image from the lens (Linear Magnification is the ratio of image height over object height. The magnification is traditionally negative if the image is inverted.)

6. What shape would you predict for a graph of magnification vs. distance of object from lens/distance of image from lens? What is the significance of the slope of this graph? Where do you expect the graph to intercept the horizontal and vertical axes? How could you use such a graph to determine the distance from a point in an object to the principal axis of the optical system, if you knew the distance from the principal axis to the corresponding point in its image

Answer 1