Up-right or Upside-down Ex. 26.2 A concave mirror has a 30 cm radius of curvature. If an object is placed 10 cm from the mirror, where will the image be found? f = R/2 = 15 cm, p = 10 cm 1/p + 1/q = 1/f  1/10 + 1/q = 1/15 3/30 + 1/q = 2/30 1/q = -1/30 q = -30 cm Case 5: p < f Real or Virtual Magnified or Reduced Up-right or Upside-down q < 0 M = -q/p = 3

Q. An upright image that is one-half as large as an object is needed to be formed on a screen in a laboratory experiment using only a concave mirror with 1 m radius of curvature. If you can make this image, I will give you $10. If you can’t you should pay me $10. Deal or no deal? Why? 1/p + 1/q = 1/f = 2/R > 0 M = -q/p = ½ > 0 should be a real image: q > 0 M = -q/p cannot be positive, if q > 0. No deal!!!

Refraction and Lenses Optical illusion: the pencil is not bent at the air-water boundary. caused by non-trivial passage of light rays.

Refraction Details, 1 Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The ray bends toward the normal

Refraction Details, 2 Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The ray bends away from the normal

The Index of Refraction When light passes from one medium to another, it is refracted because the speed of light is different in the two media The index of refraction, n, of a medium can be defined

Index of Refraction, cont For a vacuum, n = 1 For other media, n > 1 n is a unitless ratio

Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

Index of Refraction Extended The frequency stays the same as the wave travels from one medium to the other v = ƒ λ The ratio of the indices of refraction of the two media can be expressed as various ratios

All three beams (incident, reflected, and refracted) are in one plane. Snell’s Law All three beams (incident, reflected, and refracted) are in one plane. q1 q1 q2 v: speed of light in a medium n = c/v :index of refraction n > 1 v1 = c/n1, v2 = c/n2 n1sinq1 = n2sinq2

material n = c/v n depends on l. Index of Refraction vacuum 1.00 air for l = 589 nm vacuum 1.00 air 1.00029 water 1.33 ice 1.31 typical glass 1.52 polycarbonate 1.59 diamond 2.42 n depends on l. Dispersion

q1 q1 q1> q2 q2 water

Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflection

Critical Angle A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angle

Critical Angle, cont For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the boundary Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

Total internal reflection when q2 = 90 n1 (> n2) q1 n1sin(q1) = n2sin(q2) Total internal reflection when q2 = 90 sin(qc) = n2/n1 < 1 qc: critical angle

qf = 2qc Fish vision qc = sin-1(1/1.33) = 49 How could fish survive from spear fishing? Fish vision qf = 2qc qc = sin-1(1/1.33) = 49

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Q. What is the critical angle for a glass to air surface if the Index of refraction for glass is 1.5. sinqc = na/ng = 1.0/1.5 = 0.667 qc = 42

q1() q2() 10 7.5 20 14.9 30 22.0 40 28.8 50 35.0 60 40.5 70 44.8 80 47.6 sinq1/sinq2 1.33 v1 = c/n1, v2 = c/n2 n1sinq1 = n2sinq2 q1 q2 air water

A fish swims below the surface of the water A fish swims below the surface of the water. Suppose an observer is looking at the fish straight above the fish. The observer sees the fish at a greater depth than it really is. the fish at the same depth. the fish at a smaller depth than it really is. no fish due to total internal reflection.

nIIsinqII = nIIIsinqIII There are three layers of different media as shown in the figure. A beam of light bends as shown in the figure when it passes through the media. What can we say about the materials? nIsinqI = nIIsinqII qII > qI  nI > nII I nIIsinqII = nIIIsinqIII II qIII > qII  nII > nIII III nI > nII > nIII

Dispersion of Index of Refraction for Glass wavelength (nm) n 361 (near UV) 1.539 434 (dark blue) 1.528 486 (green) 1.523 589 (yellow) 1.517 656 (red) 1.514 768 (dark red) 1.511 1200 (IR) 1.505 2000 (far IR) 1.497

In glass n (red) ≈ 1.51 n (purple) ≈ 1.53

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