text: (a) Near end: Sign convention gives p = +60 cm, r = 2f = -(2 ×40) = -80 cm
  
  Negative sign indicates image is virtual, 24 cm to the right of V.Far end: p = +160 cm, r = -80 cm
  
  Far-end image is virtual, 32 cm to the right of V.
  
  ∴ Meterstick image is 32 cm - 24 cm = 8 cm long.
  
  (b) Near-end toy figure:
  
  The toy figure is 5 cm × 0.4 = 2 cm tall, at near end of the meterstick image.
  
  Far-end toy figure:
  
  The toy figure is 5 cm × 0.2 = 1 cm tall, at far end of the meterstick image.
  
  III. IMAGE FORMATION WITH LENSES
  
  Lenses are at the heart of many optical devices, not the least of which are cameras, microscopes, binoculars, and telescopes. Just as the law of reflection determines the imaging properties of mirrors, so Snell’s law of refraction determines the imaging properties of lenses. Lenses are essentially light-controlling elements, used primarily for image formation with visible light, but also for ultraviolet and infrared light. In this section we shall look first at the types and properties of lenses, then use graphical ray-tracing techniques to locate images, and finally use mathematical formulas to locate the size, orientation, and position of images in simple lens systems.
  
  A. Function of a lens
  
  A lens is made up of a transparent refracting medium, generally of some type of glass, with spherically shaped surfaces on the front and back. A ray incident on the lens refracts at the front surface (according to Snell’s law) propagates through the lens, and refracts again at the rear surface. Figure 3-20 shows a rather thick lens refracting rays from an object OP to form an image O′P′. The ray-tracing techniques and lens formulas we shall use here are based again on Gaussian optics, just as they were for mirrors.
  
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