In the thin lens approximation, a few simple rules can be used to determine the trajecto- ry of rays after the lens and thus the image formed by the lens: A ray parallel to the optical axis before the lens always passes through the focal point after the lens. A ray going through the focal point before the lens is always parallel to the optical axis after emerging from the lens. A ray passing through the centre of the lens always continues undeflected. 1.3.a. Using ray tracing in the thin lens approximation, find the image of segment AB in the two cases below (thin converging lens and thin diverging lens). B F B 1.3.b. The thin lens formula relates the position of the object along the optical axis (x) to the position of its image (x') and to the value of the focal length (f): 1 1 1 +== xx f Note: We are using here the most common form of the formula, where we assume that light is traveling from left to right, and that distances are counted starting from the lens, but in different directions for image and object: x is positive if the object is to the left of the lens, x' is positive if the image is to the right of the lens. In addition, f is positive if the lens is converging and negative if the lens is diverging. If the focal length is f+3 cm, and the distance of the object to the lens is x = 7 cm, what is the position of the image? What if the focal length is f = -3 cm, and the posi- tion of the object is x=7 cm? Are your results consistent with the ray tracing down in the previous question? 1.3.c. Are the images of segment AB formed by these lenses real or virtual? Inverted or upright? Justify your answer by using the results you obtained from both question 1.3.a and 1.3.b.