Physics 1161 Lecture 17 Refraction Lenses Textbook sections

$Physics 1161: Lecture 17 Refraction & Lenses • Textbook sections 26 -3 – 26$

Physics 1161: Lecture 17 Refraction & Lenses • Textbook sections 26 -3 – 26 -5, 26 -8

$Indices of Refraction Physics 1161: Lecture 17, Slide 2$

Indices of Refraction Physics 1161: Lecture 17, Slide 2

$Checkpoint Refraction When light travels from one medium to another the speed changes v=c/n,$

Checkpoint Refraction When light travels from one medium to another the speed changes v=c/n, but the frequency is constant. So the light bends: n 1 1 2 n 2 1) n 1 > n 2 2) n 1 = n 2 Compare n 1 to n 2. 3) n 1 < n 2

$Checkpoint Refraction Which of the following is correct? n 1 1 2 n 1$

Checkpoint Refraction Which of the following is correct? n 1 1 2 n 1 sin( 1)= n 2 sin( 2) n 2 Compare n 1 to n 2. 1) n 1 > n 2 1 < 2 2) n 1 = n 2 sin 1 < sin 2 3) n 1 < n 2 n 1 > n 2

FST & SFA • A ray of light crossing the boundary from a fast medium to a slow medium bends toward the normal. (FST) • A ray of light crossing the boundary from a slow medium to a fast medium bends away from the normal. (SFA)

$Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light$

Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light traveling through the air (n=1) is incident on water (n=1. 33). Part of the beam is reflected at an angle r = 60. The other part of the beam is refracted. What is 2? 1 r n 1 normal n 2

$Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light$

Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light traveling through the air (n=1) is incident on water (n=1. 33). Part of the beam is reflected at an angle r = 60. The other part of the beam is refracted. What is 2? 1 = r =60 1 r sin(60) = 1. 33 sin( 2) 2 = 40. 6 degrees n 1 normal n 2

$Refraction Applets • Applet by Molecular Expressions -- Florida State University • Applet by$

Refraction Applets • Applet by Molecular Expressions -- Florida State University • Applet by Fu-Kwung Hwang, National Taiwan Normal University

Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1. Medium 1 2. Medium 2 air 3. Both the same 1 2

Parallel light rays cross interfaces from air into two different media, 1 and 2, as shown in the figures below. In which of the media is the light traveling faster? 1. Medium 1 2. Medium 2 air 3. Both the same 1 2 The greater the difference in the speed of light between the two media, the greater the bending of the light rays.

Parallel light rays cross interfaces from medium 1 into medium 2 and then into medium 3. What can we say about the relative sizes of the indices of refraction of these media? 1 1. n 1 > n 2 > n 3 2. n 3 > n 2 > n 1 2 3. n 2 > n 3 > n 1 3 4. n 1 > n 3 > n 2 5. none of the above

Parallel light rays cross interfaces from medium 1 into medium 2 and then into medium 3. What can we say about the relative sizes of the indices of refraction of these media? 1 1. n 1 > n 2 > n 3 2. n 3 > n 2 > n 1 2 3. n 2 > n 3 > n 1 3 4. n 1 > n 3 > n 2 5. none of the above Rays are bent toward the normal when crossing into #2, so n > n. 2 1 But rays are bent away from the normal when going into #3, so n 3 < n 2. How to find the relationship between #1 and #3? Ignore medium #2! So the rays are bent away from the normal if they would pass from #1 directly into #3. Thus, we have: n 2 > n 1 > n 3.

$Apparent Depth • Light exits into medium (air) of lower index of refraction, and$

Apparent Depth • Light exits into medium (air) of lower index of refraction, and turns left.

Spear-Fishing • Spear-fishing is made more difficult by the bending of light. • To spear the fish in the figure, one must aim at a spot in front of the apparent location of the fish.

Apparent Depth Apparent depth: n 2 n 1 d apparent fish d actual fish 50

To spear a fish, should you aim directly at the image, slightly above, or slightly below? 1. aim directly at the image 2. aim slightly above 3. aim slightly below

To spear a fish, should you aim directly at the image, slightly above, or slightly below? 1. aim directly at the image 2. aim slightly above 3. aim slightly below Due to refraction, the image will appear higher than the actual fish, so you have to aim lower to compensate.

To shoot a fish with a laser gun, should you aim directly at the image, slightly above, or slightly below? 1. aim directly at the image 2. aim slightly above 3. aim slightly below ligh las The light from the laser beam will also bend when it hits the air -water interface, so aim directly at the fish t fr er b om eam fish

Delayed Sunset • The sun actually falls below the horizon • It "sets", a few seconds before we see it set.

Broken Pencil

Water on the Road Mirage

Palm Tree Mirage

Mirage Near Dana – Home of Ernie Pyle

Texas Mirage

Looming

Antarctic Looming

Looming

Types of Lenses

Lens Terms

Three Rays to Locate Image • Ray parallel to axis bends through the focus. • Ray through the focus bends parallel to axis. • Ray through center of lens passes straight through.

Characterizing the Image • Images are characterized in the following way 1. Virtual or Real 2. Upright or Inverted 3. Reduced, Enlarged, Same Size

Object Beyond 2 f • Image is – Real – Inverted – Reduced

Object at 2 f • Image is – Real – Inverted – Same size

Object Between 2 f and f • Image is – Real – Inverted – Enlarged

Object at F • No Image is Formed!

Object Closer than F • Image is – Virtual – Upright – Enlarged

Converging Lens Images

Beacon Checkpoint A beacon in a lighthouse is to produce a parallel beam of light. The beacon consists of a bulb and a converging lens. Where should the bulb be placed? A. Outside the focal point B. At the focal point C. Inside the focal point

Lens in Water Checkpoint Focal point determined by geometry and Snell’s Law: n 1 sin( 1) = n 2 sin( 2) P. A. n 1<n 2 F Fat in middle = Converging Thin in middle = Diverging Larger n 2/n 1 = more bending, shorter focal length. n 1 = n 2 => No Bending, f = infinity Lens in water has _____ focal length!

Lens in Water Checkpoint Focal point determined by geometry and Snell’s Law: n 1 sin( 1) = n 2 sin( 2) P. A. n 1<n 2 F Fat in middle = Converging Thin in middle = Diverging Larger n 2/n 1 = more bending, shorter focal length. n 1 = n 2 => No Bending, f = infinity Lens in water has larger focal length!

Half Lens Checkpoint A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens. 1. Only the lower half will show on screen 2. Only the upper half will show on screen 3. The whole object will still show on screen How much of the image appears on the screen?

Half Lens Checkpoint A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens.

Half Lens Checkpoint Still see entire image (but dimmer)!

Two very thin converging lenses each with a focal length of 20 cm are placed in contact. What is the focal length of this compound lens? 1. 10 cm 2. 20 cm 3. 40 cm

$Concave (Diverging) Lens • Ray parallel to axis refracts as if it comes from$

Concave (Diverging) Lens • Ray parallel to axis refracts as if it comes from the first focus. • Ray which lines up with second focus refracts parallel to axis. • Ray through center of lens doesn’t bend.

Image Formed by Concave Lens • Image is always – Virtual – Upright – Reduced

Concave Lens Image Distance • As object distance decreases – Image size increases

Image Characteristics • CONVEX LENS – IMAGE DEPENDS ON OBJECT POSITION – Beyond F: Real; Inverted; Enlarged, Reduced, or Same Size – Closer than F: Virtual, Upright, Enlarged – At F: NO IMAGE • CONCAVE LENS – IMAGE ALWAYS SAME – Virtual – Upright – Reduced

Lens Equations do di • convex: f > 0; concave: f < 0 • do > 0 if object on left of lens • di > 0 if image on right of lens otherwise di < 0 • ho & hi are positive if above principal axis; negative below

Which way should you move object so image is real and diminished? 1. Closer to the lens 2. Farther from the lens 3. A converging lens can’t create a real, diminished image. F Object F P. A.

3 Cases for Converging Lenses Past 2 F Image Object Between F & 2 F Image Object Inside F Image Object Inverted Reduced Real This could be used in a camera. Big object on small film Inverted Enlarged Real This could be used as a projector. Small slide on big screen Upright Enlarged Virtual This is a magnifying glass

Diverging Lens Principal Rays F Object P. A. F 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Image is (always true): Real or Upright or Reduced Imaginary Inverted or Enlarged

Diverging Lens Principal Rays F Object F Image 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Image is virtual, upright and reduced. P. A.

Which way should you move the object to cause the image to be real? 1. Closer to the lens 2. Farther from the lens 3. Diverging lenses can’t form real images F Object F P. A.

Multiple Lenses Image from lens 1 becomes object for lens 2 1 2 f 1 Complete the Rays to locate the final image. f 2

Multiple Lenses Image from lens 1 becomes object for lens 2 1 2 f 1 f 2

Multiple Lenses: Magnification do = 15 cm 1 2 L = 42 cm f 1 f 2 f 1 = 10 cm di = 30 cm Net magnification: di = 8. 6 cm f 2 = 5 cm do=12 cm mnet = m 1 m 2