A student is using a single thin convex lens mounted on an optical bench to investigate image formation. The lens has an unknown focal length. The student places a luminous arrow (object) along the optic axis and observes the image on a movable screen.
Throughout the investigation the student keeps the object height fixed at 2.0cm.
(a) When the object is located 40cm from the lens, the student is able to bring a sharp image into focus on the screen 10cm on the opposite side of the lens. Identify whether the image is real or virtual and whether it is upright or inverted. Justify your answer qualitatively using properties of image formation by lenses.
(b) Calculate the focal length of the lens to the correct number of significant figures and determine the numerical value of the lateral magnification for this object position.
(c) The student now moves the object gradually toward the lens while continuously adjusting the screen to keep the image sharp. Describe qualitatively how the size and orientation of the image change as the object approaches the focal point from beyond 2f to just outside f. Include a discussion of what happens to the magnification and the ease of projecting a sharp image on the screen.
(d) The student eventually places the object closer to the lens than the focal length. Explain why no real image can be obtained on the screen in this case and describe the characteristics of the image that can still be observed directly by looking through the lens.