Ch23 Geometric Optics Reflection & Refraction of Light

Reflection  Observe the reflection of a laser beam due to the mirror.  The Normal is an imaginary line drawn at a 90  angle with the surface of the mirror at the point where the beam strikes the mirror.  The angle between the incident ray and the normal is known as the angle of incidence (  i ).  The angle between the reflected ray and the normal is known as the angle of reflection (  r ). Mirror Incident RayReflected Ray Normal

Mirror Types  There are three types of mirrors: plane mirror, concave mirror, and convex mirror.  Each of these three mirror types form images with different properties.  A plane mirror forms an image that is the same size as the object.  A convex mirror form images that are smaller than the object.  A concave mirror form real images that are inverted.  What type of mirror is shown in the figure to the right?  Convex Mirror 18-2 ?????Mirror Type????? ObjectReflected Image

Diffuse Scattering.  Imagine that several parallel laser beams are fired at a mirror and a ceiling tile.  The reflected beams from the mirror surface would still be parallel, and  i and  r would be equal.  However, the reflected beams from the tile surface would not be parallel.  The reflected beams from the tile surface exhibit diffuse scattering Mirror Ceiling Tile

Formation of Images by Spherical Mirrors We use ray diagrams to determine where an image will be. For mirrors, we use three key rays, all of which begin on the object: A ray parallel to the axis will be reflected through the focal point A ray through the focal point will be reflected parallel to the axis A ray perpendicular to the mirror will be reflected back on itself

cf Concave: Object outside of C Image is: Inverted Smaller Between C & F Real

cf Concave: Object is between C & F Image is: Inverted Larger Outside of C Real

c f Concave: Object is at C Image is: Inverted Same size At C Real

cf Concave: Object is at f

c f Concave: Inside of f Image is: Up right Larger Behind the mirror virtual

c f Convex: Image is: Up right Smaller Behind the mirror virtual

23.3 Formation of Images by Spherical Mirrors Geometrically, we can derive an equation that relates the object distance, image distance, and focal length of the mirror: (23-2)

23.3 Formation of Images by Spherical Mirrors We can also find the magnification (ratio of image height to object height). (23-3) The negative sign indicates that the image is inverted.

 Simply put, “Refraction” means bends.  When discussing light beams, light bends when it goes from one medium (glass, water, air, etc.) to another.  If it goes from a more dense medium to a less dense medium, then light speeds up and bends away from the Normal.  If it goes from a less dense medium to a more dense medium, then light slows down and bends towards the Normal.  Consider the wheel and axel to the right.  It rolled from pavement (faster) to gravel (slower)  The left wheel slowed down causing the axel to turn towards the normal. Pavement Gravel Refraction

 When light undergoes refraction while traveling from a less dense to a more dense medium, the light bends towards the normal.  This is because light travels faster in a less dense medium than in a more dense medium.  Is the fish safe from the laser if we point the laser at the fish? Normal

Refraction  Which of the three paths (A, B, or C) is the one the beam would actually travel?  Remember, lights bends towards the normal when it goes from a less dense to a more dense medium because it slows down in the more dense medium.  Which is the correct path? A B C Air Glass Water

Snell’s Law  Snell’s law allows us to determine the angle of refraction given the angle of incidence of a light ray on a boundary interface.  Based upon the picture to the right, which medium is more dense: 1 or 2? Why?  Because medium 2 is more dense n 2 >n 1. n 1 sin  1 = n 2 sin  2 n1n1 n2n2

Index of Refraction, n  The index of refraction is a ratio of the speed of light in a vacuum (c) to the speed of light in a medium (v) like glass, oil, water, quartz, diamond,….  The top figure shows a laser aimed into a evacuated cylinder (nothing is inside it).  The speed of light in this cylinder is c = 3 x 10 8 m/s.  The bottom figure shows a laser aimed into a cylinder of water.  The light will travel slower in this cylinder, and its speed (v) can be measured in a lab.  The ratio of these speeds gives the index of refraction (n) of the material through which the light is shined (in this case water). 1

Internal Reflection  Suppose we had a laser submerged in water.  If it was pointing straight up, then the beam would pass through the boundary interface without reflecting or refracting.  If we rotate the laser, then some of the beam will reflect and some will refract.  This phenomena occurs at the critical angle.  As the laser is rotated past the critical angle, all of the beam will be reflected and none will be refracted.  This phenomena is known as total internal reflection.

Lens Vocabulary  A – Center of Curvature  B – Focal Point  C – Focal Length  D – Principal Axis AABB CC D

f f ’ An object is located in front of a diverging lens Where is the image located?

Magnification Magnification is the enlargement or reduction of the size of the image of an object produced by a lens. If the object is beyond twice the focal length (2f), then the image will be smaller, real, and inverted If the object is at 2f, the it will be the same size and real. Between f and 2f, the object will be larger and real. At f the image will focus at infinity (not be visible). In between f and the lens, the image will be much larger, virtual, up right.

Lenses and Magnification – Converging Lens Real or virtual? The focal length is positive for converging lenses

Lenses and Magnification – Diverging Lens Real or virtual? The focal length is negative for diverging lenses

23.3 Formation of Images by Spherical Mirrors We can also find the magnification (ratio of image height to object height). (23-3) The negative sign indicates that the image is inverted.

Light Spectrum Light is composed of massless particles known as photons. The spectrum of electromagnetic radiation spans several wavelengths (frequencies) of the photons. Of particular interest to us is the visible spectrum. To remember the visible spectrum, use the name “ROY G BIV.” VisibleInfraredUltra VioletGammaRadio WavesMicrowavesX-rays Red Orange Yellow Green Blue Indigo Violet Frequency Increases Wavelength Increases

Dispersion of Light Dispersion is the separation of light according to its frequencies into its different colors. A prism is a device often used to demonstrate dispersion of white light. Light with higher frequency travels slower in a medium; therefore, it will bend more with respect to the normal. Light with lower frequency travels faster; therefore, it will bend less with respect to the normal. Red Orange Yellow Green Blue Indigo Violet Frequency Speed 18-13