Question

need help with the first range, for some reason I can't seem to solve for the correct answer. Thanks!

Lens L1 in the figure below has a focal length of 14.1 cm and is located a fixed distance in front of the film plane of a camera. Lens L2 has a focal length of 12.5 cm, and its distance d from the film plane can be varied from 5.00 cm to 10.0 cm. Determine the range of distances for which objects can be focused on the film Objects can be focused on the film from Your response differs from the correct answer by more than 10%. Double check your calculations. m to 1.75 Film 12.0 cm

Answer 1

Given that The focal length f_1 = 14.1 cm focal length f_2 = 12.5 cm The distance d varies from 5 cm to 10 cm Since the final image to be real in the film plane the image distance from lens 2 is q_2 = + d thus the object position from L_2 is P_2 = q_2 f_2/q_2 - f_2 = d f_2/d - f_2 = 12.5 d/d - 12.5 Since d proportionalto f_2 therefore P_2 < 0 So the object of second lens is a virtual object if q is the image distance of lens 1 then q_1 = (12 - d) - P_2 = (12 - d) - d f_2/d - f_2 = (12 - d) [1 + f_2/d - f_2] = 12 - d^2/d - f_2 \r\n implies if d = 5 then q_1 = 12 - 5^2/5 - 12.5 = 12 - 25/- 7.5 = 12 - (- 3.33) = 12 + 3.33 = 15.33 cm implies if d = 10 then q_1 = 12 - (10)^2/10 - 12.5 =