Geometrical optics 4.1 Reflection and Refraction In geometrical optics light waves are considered to move in straight lines. • Geometrical Optics This is a good description as long as the • Reflection waves do not pass through small openings (compared to λ) • Refraction
Christian Huygens
Light waves Rays are perWpeanvdiecula front r to wave fronts
perpendicular to wave fronts
Rays are not physical entities but are a convenient representation of a light wave.
(surfaces with constant phase e.g. maxima)
Specular reflection Diffuse reflection Reflection Rough surface Flat surface Light reflected in all directions Light reflected in one direction • Two general types of reflection – Specular reflection – Diffuse reflection • Most of geometric optics deals with specular reflection. • However, most of the time ambient lighting is due to diffuse reflection.
1 Transmission and Reflection at an What are some examples of these processes in this interface picture.
Reflection Transmission Specular Reflection Absorption x Incident wave Diffuse reflection (scattering)
medium 1 medium 2 Transmission Absorption
Law of Reflection Full length mirror The angle of reflection equals the angle of incidence A 6 ft tall man wants to install a mirror tall enough to see his ' whole body. How tall a mirror is needed? θ1 = θ1
Angle of incidence Angle of reflection
Reflecting surface
Multiple reflections 2Dimensional Corner reflector
Mirror 2 Show that 2 perpendicular mirrors reflect • For multiple reflections use the law of a light beam in a plane perpendicular to both reflection for each reflecting surface. mirrors back along the opposite direction 1
r o irr M
2 Refraction Refraction and Reflection • Refraction is the bending of light when it passes across an interface between two materials. • The bending is due to the differences in the speed of light in different media.
The light beam (3) is refracted at the interface.
Speed of light in a medium Transmission across an interface
medium vacuum The speed of the wave changes. The frequency remains the same. The wavelength changes c v slower
c Index of refraction n = v
Snell’s Law of Refraction
n1 sinθ1 = n2 sin θ 2
Going from air to glass
n 2 > n 1
θ2 < θ1
(sinθ increases with θ )
3 Physical picture for Snell’s Law
One end of the wave front slows down. Going from glass to air The wave front changes direction.
n 2 < n 1
θ2 > θ1
Example Example
Find the angle of refraction for Show that light going through an angle of incidence of 30 o in a flat slab is not deviated in going from air to glass angle.
(n glass =1.52)
question Problem
When light goes from air into glass the angle The cylindrical tank in a public aquarium is 10 m deep, 11 m in diameter, and full to the brim with water. If a of refraction is ______the angle of flashlight shines on the tank from above what is the incidence. minimum angle its beam can make with the horizontal if A) greater than it is to illuminate part of the tank bottom? B) less than C) equal to
4 Refractive index matching
• A transparent object can be made invisible if the index of refraction of the surrounding media is made the same as that of the object.
5