Phy2005 Applied Physics II Spring 2017 Announcements: Exam and updated HITT grades posted on Canvas

For a small object, f = R/2 (spherical mirror) Last time: Mirror Equation 1/p + 1/q = 1/f For a small object, f = R/2 (spherical mirror) 1/p + 1/q = 2/R Alert!! Be careful with the sign!! Negative means that it is behind the mirror!! p defined to be positive negative q means virtual image How about f?

Focal point inside the mirror Last time For a concave mirror: f > 0 Convex mirror: Focal point inside the mirror f < 0 1/p + 1/q = 1/f < 0 : q should be negative. Magnification, M = -q/p Negative M means that the image is upside-down. For real images, q > 0 and M < 0 (upside-down).

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

Who has the better chance to save this drowning guy? Pam Anderson, whose path takes the shortest time Li David Hasselhoff Jeremy Jackson Pamela Anderson Light travels the path that takes the shortest time between two points

All three beams (incident, reflected, and refracted) are in one plane. v: speed of light in a medium < c n = c/v :index of refraction n > 1 Snell’s Law All three beams (incident, reflected, and refracted) are in one plane. q1 q2 air glass 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

Apparent position and actual position are different due to refraction.

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

Example: fisheye view air/water interface qfisheye = 2qc qfisheye = angular range fish can see qc = sin-1(1/1.33) = 49

Optical Fiber Total internal reflection! ncore nclad >

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

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Q2 A fish swims below the surface of the water Q2 A fish swims below the surface of the water. Suppose an observer is looking at the fish from the side. The observer sees the fish at a greater depth than it really is. the fish at its actual depth. the fish at a smaller depth than it really is. no fish due to total internal reflection.

Q3 A fish swims below the surface of the water Q3 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 its actual depth. the fish at a smaller depth than it really is. no fish due to total internal reflection.

Clicker Quiz Time Log in your remote! ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions. Log in your remote!

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 relative index of refraction of these materials? The media I-II-III have indices of refraction that get smaller 2) One of the media is a vacuum 3) One of the media is glass 4) The media I-II-III have indices of refraction that get bigger 5) Two of the media are the same I II III

nIIsinqII = nIIIsinqIII qII > qI  nI > nII nIsinqI = nIIsinqII nIIsinqII = nIIIsinqIII qII > qI  nI > nII qIII > qII  nII > nIII nI > nII > nIII I II III

“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

Air Water

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

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What is the angle between the red (4.6x1014 Hz) and blue (6.3x1014 Hz) rays emerging from a 30o prism as shown? n, quartz 1.48 1.47 30o white 1.46 q 1.45 300 500 700 l(nm) sin q = n sin 30o = n/2 Ans: 0.004 Radian = 0.23o