Lecture 16 Thin Lenses – Ray Tracing

LECTURE 16 THIN LENSES – RAY TRACING

Instructor: Kazumi Tolich Lecture 16

¨ 18.4 Image formation by refraction

¨ 18.5 Thin lenses: ray tracing ¤ Converging lenses ¤ Real images ¤ Magnification ¤ Virtual images ¤ Diverging lenses Quiz: 18.4-1

¨ Suppose that you are inserting a ruler in an aquarium filled with water.

¨ The distance to the ruler in water appears to be A. Less than the actual distance. B. Equal to the actual distance. C. More than the actual distance. Quiz: 18.4-1 answer

¨ The distance to the ruler in water appears to be less than the actual distance because of refraction of light at the boundary.

¨ To your eye, the rays appear to diverge not from the object at point P, but instead from point P¢. 18.4 Image formation by refraction

¨ The optical axis is the line through the object and perpendicular to the boundary.

¨ Using Snell’s law and geometry, you can show that the image distance is given by

� � = � � 18.5 Thin lenses: ray tracing

¨ A lens uses refraction of light rays at curved surfaces to form an image.

¨ Ray tracing is a pictorial method used to understand image formation. Quiz: 18.5-1

¨ You can use the sun’s rays and a lens to start a fire. To do so, you should use A. a converging lens. B. a diverging lens. C. either a converging or a diverging lens will work if you use it correctly. Quiz: 18.5-1 answer / Demo

¨ You can use the sun’s rays and a lens to start a fire. To do so, you should use a converging lens. The energy in the sun’s rays can be focused and concentrated.

¨ A converging lens causes the rays to refract toward the optical axis.

¨ A diverging lens causes the rays to refract away from the axis.

¨ Demo: diverging and converging lenses 18.5 Thin lenses: ray tracing – focal point and focal length

¨ The incoming rays parallel to the optical axis converge at (converging lens) or appear to diverge from (diverging lens) the focal point of the lens.

¨ The focal point on the incident-light side is the near focal point; the focal point on the other side is the far focal point.

¨ The focal length � of the lens is the distance of the focal point from the lens. 18.5 Converging lenses

¨ A thin lens is an idealized lens whose thickness is zero and that lies entirely in a plane called the lens plane.

¨ Within the thin-lens approximation, all refraction occurs as the rays cross the lens plane, and all distances are measured from the lens plane.

¨ The special rays for a converging lens: Quiz: 18.5-2

¨ Which of these ray diagrams is possibly correct for a thin glass lens in air? Quiz: 18.5-2 answer

¨ A lens that is thick in the middle is a converging lens if the lens is made with a material of a higher index of refraction than that of the surrounding.

¨ A ray directed at the center of the lens passes through in a straight line. Quiz: 18.5-3

¨ A converging lens is used to project the image of an arrow onto a screen. If the arrow is farther away from the lens than its focal length, what kind of image is projected on the screen? Choose all that apply. A. Real B. Virtual C. Upright D. Inverted E. No image can be projected. Quiz: 18.5-3 answer / Demo

¨ Real and inverted

¨ A real image is formed where rays converge. A real image is always inverted.

¨ All points on the object plane converge to image points in the image plane.

¨ When a screen is placed in the image plane, the image is sharp and well-focused.

¨ Demo: Image formation Quiz: 18.5-4

¨ A piece of black tape is now placed over the upper half of the converging lens. Which of the follow is true? A. Only the lower half of the object (i.e., the arrow tail) will show on the screen. B. Only the upper half of the object (i.e., the arrow head) will show on the screen. C. The whole object will still show on the screen. Quiz: 18.5-4 answer / Demo

¨ The whole object will still show on the screen.

¨ The image will be dimmer because only half of the light now go through the lens.

¨ A smaller lens “collects” less rays, and therefore makes a dimmer image.

¨ Demo: Image formation with a half-covered lens 18.5 Magnification

¨ The magnification � describes the orientation and size of the image relative to the object and its size.

� � = − �

¤ � = is the ratio of image height to object height. ¤ If � > 0, the image is upright relative to the object. ¤ If � < 0, the image is inverted relative to the object. 18.5 Virtual images

¨ When the object is inside the focal point of a converging lens, the refracted rays do not converge.

¨ Rays appear to diverge from a virtual image.

¨ Because no rays actually pass through a virtual image, placing a screen at the image plane would not produce an image.

¨ We use a sign convention defining the image distance � to be negative for a virtual image. 18.5 Diverging lenses

¨ The special rays for a diverging lens: Quiz: 18.5-5

¨ When a real object is placed just outside the focal point of a diverging lens, what kind if image is formed? Choose all that apply. A. Diminished. B. Enlarged. C. Upright. D. Inverted. E. Real. F. Virtual. Quiz: 18.5-5 answer

¨ Diminished, Upright, Virtual. ¨ Draw ray diagram to deduce where the image is formed. ¨ A diverging lens always create diminished, upright, and virtual images. Quiz: 18.5-6

¨ A diverging lens is often made of glass with two concave surfaces (as shown). If instead the same shape were filled with air, and it was placed in water which of the following statements is correct? A. Nothing acts as a lens inside water. B. It will act as a diverging lens. C. It will act as a converging lens. D. Not enough information given. Quiz: 18.5-6 answer / Demo

¨ It will act as a converging lens. Focus ¨ We can consider the wave fronts. The wave front moves faster through the air in the lens, so the top and bottom move Wavefronts more than the middle. An air lens in water ¨ Demo: Air lens in water

A glass lens in air