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Physics 123

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23. Light: Geometric Optics 23.1 The Ray Model of Light 23.2 Reflection - Plane Mirror 23.3 Spherical Mirrors 23.5 Refraction - Snell’s law 23.7 Converging and Diverging Lenses

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Reflection ii rr i = r Angle of incidence equals the angle of reflection

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Image in a Plane Mirror

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d o = d i

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Spherical Mirrors Concave mirror Convex mirror

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Concave Mirror radius = r focus = f r f f = r / 2

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Concave Mirror A parallel ray reflects through the focus

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Concave Mirror Solar Cooker!

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Concave Mirror A ray through the focus reflects parallel

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Concave Mirror Image is inverted, real, reduced

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Concave Mirror Equation 1 / d o + 1 / d i = 1 / f

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Concave Mirror Problem A 3 cm high candle is located 5 cm from a concave mirror whose radius of curvature is 20 cm. What are the characteristics of the image?

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Concave Mirror Problem f = 10 cm 1/d o + 1/ d i = 1/f 1/5 + 1/ d i = 1/10 1/ d i = - 1/10 d i = - 10 cm The image is 10 cm behind the mirror, virtual, upright, and magnified 2X m = - d i / d o

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Concave Mirror Problem Makeup mirror! If the object is within the focus of the concave mirror the image is enlarged (magnified), upright but virtual … it’s all in your head!!!

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Convex Mirror

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Image will ALWAYS be reduced, virtual, upright

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Jurassic Park! Rear View Mirror Objects in the mirror are closer than they appear!

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Convex Mirror Equation 1 / d o + 1 / d i = 1 / f Note: f is negative d i is negative

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Convex Mirror Problem A 3 cm high candle is located 5 cm from a convex mirror whose radius of curvature is 20 cm. What are the characteristics of the image?

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Convex Mirror Problem f = - 10 cm 1/d o + 1/ d i = 1/f 1/5 + 1/ d i = - 1/10 1/ d i = - 3/10 d i = - 3.3 cm The image is 3.3 cm behind the mirror, virtual, upright, and reduced in size m = - d i / d o m = 1 / 3

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Refraction ii rr

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Index of Refraction n = sin i / sin r

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Refraction Problem The index of refraction of glass is 1.5. A ray of light is incident on a glass pane at an angle of 60 0. Calculate the angle of refraction.

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Refraction Problem n = sin i / sin r 1.5 = sin 60 0 / sin r 1.5 = 0.866 / sin r sin r = 0.866 / 1.5 sin r = 0.58 r = 35 0

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Converging (convex) Lens

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Converging Lens When the object is outside the focus, the image is real and inverted

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Converging Lens When the object is inside the focus, the image is virtual, upright, and enlarged.

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Diverging (concave) Lens

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The image is ALWAYS reduced, upright, virtual

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Lens Problem A 35 mm slide projector uses a converging lens with f = 20 cm. The screen is 3 m away. How far is the slide from the lens?

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Lens Problem 1/d o + 1/ d i = 1/f 1/d o + 1/ 300 = 1/20 1/d o = 1/20 - 1/ 300 d o = 21. 4 cm m = - d i / d o m = - 300 / 21.4 m = -14 Image is real, inverted, magnified

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That’s all folks!

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