Two Lens System with Diverging Lens 1 2 3 4 7 A system of two lenses forms an image of an arrow at x = *3 = 55.1 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude fy = 8.5 cm. The second lens is located at x = x2 = 23.8 cm and has an unknown focal length. The tip of the object arrow is located at (x. yl = (ky. yo) = (-33.8 cm, 24.3 cm). (x . y.) 1) What is x, the x co-ordinate of image of the arrow formed by the first lens? cm Submit 2) What is y, the y co-ordinate of the image of the tip of the arrow formed by the first lens? cr Submit ") What is fy, the focal length of the second lens. If the lens is a converging lens, fy is positive. If the lens is a diverging Lens, fo is negative. cm Submit 4) What is ya. the y co-ordinate of the image of the tip of the arrow formed by the two lens system? cm Submit 5) The positions of the two lenses are now interchnaged (i.e., the second lens is moved to x = 0 and the diverging lens is moved to x = x, = 23.8 cm). What is the nature of the final image in this new system? Real and Inverted Real and Upright O Virtual and Inverted O Virtual and Upright SubmitTwo Lens System 1 2 3 4 7 A diverging lens located in the y-z plane at x = 0 forms an image of an arrow at x = X, = -20.9 cm. The image of the tip Ay of the arrow is located at y = y2 = 3.9 cm. The magnitude of the focal length of the diverging lens is 58.1 cm. light ( X2 , )2) image 1) What is x , the x co-ordinate of the object arrow?. cm Submit +) 2) What is y1, the y co-ordinate of the tip of the object arrow? cm Submit +3) A converging lens of focal length fconverging = 11.22 cm is now inserted at x = x; = -17.3 cm. In the absence of the AY diverging lens, at what x co-ordinate, *4, would the image of the arrow form? light image in absence of diverging lens XA cm Submit 4) To determine the image of the arrow from the combined converging + diverging lens system, we take the image from the converging lens (in the absence of the diverging lens) to be the object for the diverging lens. If this image is downstream of the diverging lens, the object for the diverging lens is virtual. All this means is that the rays entering the diverging lens are converging towards a location downstream of the diverging lens. The final image can be calculated using this virtual object distance and the focal length of the diverging lens. If this description seems unclear to you, you can check out the more detailed description of multiple lens systems given in the Optical Instruments unit. What is x, the x co-ordinate of the final image of the combined system? cm Submit 5) Is the final image of the arrow real or virtual? Is it upright or inverted? Real and upright Real and inverted O Virtual and upright O Virtual and inverted SubmitA spherical mirror forms an image of an arrow at x = x7 = -72.7 cm. The mirror is represented in the drawing as a Ay plane at x = 0. The tip of the object arrow is located at (x,y) = (x.y,) = (-94 cm, 7.73 cm). 1) What is f, the focal length of the mirror? If the mirror is concave f is positive. If the mirror is convex, f is negative. 40.9046 cm Submit 2) What is ya, the y co-ordinate of the image of the tip of the arrow? -5.97 cm Submit 3) The object arrow is now moved such that image distance doubles, i.e.. >mage,now = -145.4 cm. What is Yimage,new" the new y co-ordinate of the image of the tip of the arrow? 57.102 cm Sulamit () The object arrow is now moved to x = $1new = -18.4 cm. What is yz,now. the new y co-ordinate of the image of the anraw? cm Submit 5) Which of the rays in the diagram is not reflected as shown? (a) . (b)- O (a) O (c) Submit