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Geometrical Optics and Lenses

Geometrical Optics and Lenses. Snell’s Law Examples of Snell’s Law Total Internal Reflection Fiber Optics www.cmog.org (Corning NY) Ray Tracing and Thin Lenses Example – real image Example – inverted image Sign Rule and Summary. Index of Refraction.

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Geometrical Optics and Lenses

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  1. Geometrical Optics and Lenses • Snell’s Law • Examples of Snell’s Law • Total Internal Reflection • Fiber Optics www.cmog.org (Corning NY) • Ray Tracing and Thin Lenses • Example – real image • Example – inverted image • Sign Rule and Summary

  2. Index of Refraction • Ratio of speed in vacuum to speed in medium • Important when passing from one medium to another • Light’s speed in diamond (n=2.42) • Index of refraction of various materials <table 23-1>

  3. Snell’s Law - Refraction • Governs how light ray goes from one medium to another • Snell’s Law • Toward normal in faster medium • Person in swimming pool • Also Reflection Law

  4. Refraction through flat glass Light travelling in air strikes a flat piece of uniformly thick glass at an incident angle of 60°.If the index of refraction is 1.5, what is the angle of refection θa in the glass, and the angle θb at which the rays emerges from the glass? • For the angle in the glass θa • For the angle in the glass θa • Emerges at the same angle it went in

  5. Apparent depth of pool A swimmer has dropped her goggles to the bottom of the pool at the shallow end, marked as 1.0 m deep. But the goggles don’t look that deep. Why? How deep to the goggles appear to be? • Snell’s Law • But θair is angle light appears to be coming from! • Since sinθ≈θ≈tanθ for small angles, so

  6. Critical Angle • Going from high to low index θ increases • Sinθ2 = 1 determines maximum angle θ1 that can be transmitted! • Critical angle for water • Fiber optics makes use of Critical angle

  7. Light Bending at thin lens • Thin lens • Principal axis • Focal point • Air-glass interface • Entering glass bent toward normal (down) • Leaving glass bent away from normal (also down)

  8. Real image at thin lens

  9. Example – Converging Lens What is • the position, and di = 5.26 cm • the size, m = -.0526 hi = -.40 cm of a 7.6 cm high flower placed 1.0 m from a 50 mm focal length camera lens? Image real and inverted

  10. Example - Close to converging lens An object is place 10 cm from a 15 cm focal length converging lens. Determine the image • position and di = -30cm • size. m = 3 Image virtual and upright

  11. Sign convention

  12. Diverging Lens Where must a small insect be placed if a 25 cm focal length diverging lens is to form a virtual image 20 cm in front of the lens? do = 100 cm

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