A woman cannot see objects closer than 40 cm from her left eye and closer than 100 cm from her right eye. During a hiking expedition, she is separated from her group. She attempts to build an astronomical telescope from her reading glasses to look for her companions. What magnification can she achieve with a relaxed eye?

Step-by-step solution

For reading glasses, the object distance is taken as the standard near point, u = -25 cm . The lenses form virtual images at the respective near points of the defective eyes. For the left eye, the image distance is v_L = -40 cm . Using the lens formula: 1 f_L = 1 v_L - 1 u 1 f_L = 1 -40 - 1 -25 = -5 + 8 200 = 3 200 cm ⁻¹ f_L = 200 3 cm For the right eye, the image distance is v_R = -100 cm . Using the lens formula: 1 f_R = 1 v_R - 1 u 1 f_R = 1 -100 - 1 -25 = -1 + 4 100 = 3 100 cm ⁻¹ f_R = 100 3 cm An astronomical