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. Which lens should she use as the eyepiece?

Step-by-step solution

The woman is suffering from hypermetropia, so she uses convex lenses for reading. For the left eye, the near point is 40 cm . Using the lens formula with v = -40 cm and u = -25 cm : 1 f_ L = 1 v - 1 u = 1 -40 - 1 -25 = 3 200 cm ⁻¹ f_ L = 200 3 cm For the right eye, the near point is 100 cm . Using the lens formula with v = -100 cm and u = -25 cm : 1 f_ R = 1 v - 1 u = 1 -100 - 1 -25 = 3 100 cm ⁻¹ f_ R = 100 3 cm Since f_ L > f_ R , the left lens has a larger focal length than the right lens. In an astronomical tele