Question
The lens combination as shown in the figure, consists of two lenses, L_1 and L_2, of the focal lengths +10 cm and -10 cm, respectively. The position of the image formed is :
The lens combination as shown in the figure, consists of two lenses, L_1 and L_2, of the focal lengths +10 cm and -10 cm, respectively. The position of the image formed is :
C. 60 cm to the left of the concave lens
For the first lens L_1 (convex lens): Object distance, u_1 = -30 cm Focal length, f_1 = +10 cm Using the lens formula, 1 v_1 - 1 u_1 = 1 f_1 1 v_1 - 1 -30 = 1 10 1 v_1 + 1 30 = 1 10 1 v_1 = 1 10 - 1 30 = 3 - 1 30 = 2 30 = 1 15 v_1 = +15 cm The image I_1 formed by L_1 acts as a virtual object for the second lens L_2. For the second lens L_2 (concave lens): Distance between the lenses, d = 3 cm Object distance for L_2, u_2 = v_1 - d = 15 - 3 = +12 cm Focal length, f_2 = -10 cm Using the lens formula, 1 v_2 - 1 u_2 = 1 f_2 1 v_2 - 1 12 = 1 -10 1 v_2 = 1 12 - 1 10 = 5 - 6 60 = - 1 60 v_2 = -60 cm The negative sign indicates that the final image is formed 60 cm to the left of the concave lens. Answer: 60 cm to the left of the concave lens
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