Final answer:
The independent variable in the study is the lighting conditions, while the dependent variable is the length of time taken to identify the image. The plot of light intensity versus time taken would not be a straight line; however, plotting light intensity versus the reciprocal of the square of the time taken could result in a straight line if the inverse square law holds.
Step-by-step explanation:
In the study described, the independent variable is C) The lighting conditions (low, moderate, high). The independent variable is the factor that is manipulated or controlled by the experimenter to determine its effect on the dependent variable. In this case, the lighting conditions are being changed to observe how they affect the time taken by participants to identify the image. The dependent variable is A) The length of time taken to identify the image, as it is what is being measured and is expected to change in response to the different lighting conditions.
To answer part d. and e. of your question regarding the relationship between light intensity and efficiency, if the study measured how changes in light intensity affected the length of time taken to identify an image and the inverse square law was upheld, the plot of the independent variable versus the dependent variable would not be a straight line. Instead, if light intensity was plotted on the x-axis and the time taken was plotted on the y-axis, the resulting graph would show a curve that reflects the inverse square relationship. However, if the plot were of light intensity versus the reciprocal of the square of the time taken (or vice versa), then the plot could be a straight line, as this would linearize the inverse square relationship.