Optics Reflection and Refraction Lenses

REFLECTIONREFRACTION DIFFRACTIONINTERFERENCE Fundamentals of Optics Continuum of wavesFinite no. of waves IMAGING POLARISATION EM-theory

Refraction, Reflection, and Diffraction Reflection – Waves bounce off a surface Refraction- Waves bend when they pass through a boundary Diffraction- Waves spread out (bend) when they pass through a small opening or move around a barrier.

Reflection When a wave encounters a barrier, it can reflect or the bounce off of the obstacle. Examples: Light – MirrorsSound - Echo Most objects we see reflect light rather than emit their own light. Fermat's principle - light travels in straight lines and will take the path of least time MIRROR AB Wrong Path True Path

Law of Reflection The Law of Reflection states :The angle of incidence equals the angle of reflection.  i =  r This is true for both flat mirrors and curved mirrors.

Calm water can provide for the specular reflection of light from the mountain creating an image of the mountain on the surface of the water.

Mirror Image We trace rays from the object The image formed by the plane mirror is called a virtual image The image is the same distance behind the mirror as the object is in front of it The object and the image are the same size

Refraction When one medium ends and another begins, that is called a boundary. When a wave encounters a boundary that is more dense, part of it is reflected and part of it is transmitted The frequency of the wave is not altered when crossing a barrier, but the speed and wavelength are. The change in speed and wavelength can cause the wave to bend, if it hits the boundary at an angle other than 90°.

Refraction for Light Waves For light waves, this bending as light enters the water can cause objects under water to appear at a different location than they actually are. Water Fish in the water appear closer and nearer the surface. n – index of refraction: n = speed of light in a vacuum/ speed of light in material n 2 = 1.0 n 1 = 1.33 22 11 The index of refraction gives the speed of light in a medium:

Critical Angle At an interface, when light is going from a region of high refractive index (lower speed) to lower index (higher speed), the light is bent away from the normal If the angle of incidence gets great enough it will be bending away at 90 o This is called the critical angle

Total Internal Reflection Once the angle of incidence is larger than the critical angle, the light cannot escape the higher index material This means that all the light is reflected from the surface back into the higher index material This is total internal reflection

12 Lenses are used to focus light and form images. There are a variety of possible types; we will consider only the symmetric ones, the double concave and the double convex.

13 Converging Lens Diverging Lens

14 A ray diagram uses three rays to find the height and location of the image produced by a lens. The three principal rays for lenses are similar to those for mirrors: The P ray—or parallel ray—approaches the lens parallel to its axis. The F ray is drawn toward (concave) or through (convex) the focal point. The midpoint ray ( M ray) goes through the middle of the lens. Assuming the lens is thin enough, it will not be deflected. This is the thin-lens approximation.

15 Ray Tracing for Lenses

16 note: C = 2f, where f is the focal point

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22 The thin-lens approximation and the magnification equation:

23 Sign conventions for thin lenses:

Example 1 An object is placed 20 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image? Real image, magnification = − 

Example 2 An object is placed 5 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image? Virtual image, as viewed from the right, the light appears to be coming from the (virtual) image, and not the object. Magnification = +2

Diffraction Diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path.

Diffraction of Sound and Light Waves Sound waves bend around obstacles and bend when passing through an opening making it possible to hear sound outside an open door or behind an obstacle. Light waves also bend around obstacles and when passing through an opening creating a diffraction pattern on a screen.

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