(a) As shown in Fig. la, the object and the screen is separated by 1 = 100cm. When we put a convex lens in the middle point between the object and the screen, a clear image is formed on the screen. What is the focal length of the lens? You may use either ABCD matrix or other methods. 100cm Fig. la (b) Now we replace the lens in (a) with an unknown lens (focal length f), as shown in Fig. 1b. Assume the distance between the object and the lens is S cm, what is the ABCD matrix from the object to the screen? What can we know about this matrix if a clear image is formed on the screen? 100cm P1 20cm P2 Fig. 1b (c) When we move the lens back and forth, we find that there exist two positions (Pl and P2 as shown in Fig. 1b) where clear image can be formed on the screen. The separation between the two positions is measured to be 20 cm. Is the unknown lens convex or concave? What is the focal length? Hint: The solution of a quadratic equation ax +bx+c=0 is -b±yb² – 4ac 2a

(a) As shown in Fig. la, the object and the screen is separated by 1 = 100cm. When we put a convex lens in the middle point between the object and the screen, a clear image is formed on the screen. What is the focal length of the lens? You may use either ABCD matrix or other methods. 100cm Fig. la (b) Now we replace the lens in (a) with an unknown lens (focal length f), as shown in Fig. 1b. Assume the distance between the object and the lens is S cm, what is the ABCD matrix from the object to the screen? What can we know about this matrix if a clear image is formed on the screen? 100cm P1 20cm P2 Fig. 1b (c) When we move the lens back and forth, we find that there exist two positions (Pl and P2 as shown in Fig. 1b) where clear image can be formed on the screen. The separation between the two positions is measured to be 20 cm. Is the unknown lens convex or concave? What is the focal length? Hint: The solution of a quadratic equation ax +bx+c=0 is -b±yb² – 4ac 2a