Refraction and Lenses

Refraction The bending of light when it enters a different medium at an angle due to a change in speed. Light slows down and bends toward the normal when entering a more optically dense medium (greater n). Light speeds up and bends away from the normal when entering a less optically dense medium (smaller n). Air (n = 1.00) Glass (n=1.50) Glass (n=1.50) Air (n = 1.00)

Snell’s Law normal incident ray Air (ni =1.00) i n = index of refraction for the medium Boundary refracted ray r Water (nr = 1.33) Angles are always measured from the normal, never the surface

ni = index of refraction of incident medium θi = angle of incidence, degrees nr = index of refraction of refracting medium θi = angle of refraction, degrees

Index of Refraction Light changes speed (v) as it enters a new medium In a vacuum the speed of light (c) is 3.0 x 108m/s The index of refraction (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material. Index of refraction has no units! The larger the n, the slower the light speed.

Critical Angle The angle of incidence that causes the angle of refraction to be 90o The refracted ray is tangent to the boundary between mediums Only possible when going from a more optically dense (high index of refraction) to less optically dense medium (low index of refraction) ni > nr c r=900 n=1 n=1.5

Critical Angle  

Total Internal Reflection When the angle of incidence exceeds the critical angle, the light does not cross the boundary into the new medium or refract. All of the light is reflected back into the incident (denser) medium according to the Law of Reflection (angle of incidence = angle of reflection) Application – fiber optic cables

Total Internal Reflection Angle of incidence > critical angle and ni > nr Angle of incidence = Angle of reflection      

Prisms Makes white light split up or disperse into the color spectrum The index of refraction depends on the wavelength of light so different colors of light bend or refract at different angles.

Dispersion The process of separating white light into its component wavelengths (or colors). As wavelength decreases, the index of refraction increases. Blue light refracts more than red light since it has a shorter wavelength and thus a larger index of refraction.

Diffraction The bending or spreading out of a wave (including light) in the region behind an obstruction as the waves go around it or through an opening between obstructions.

Concave Lenses Thinner in the middle than at the edges. Parallel rays of light from a far object will refract through the lens and diverge as if they came from the focal point in front. Concave lenses are also called “diverging lenses”. Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

Convex Lenses Thicker in the center than at the edges Parallel rays of light from a far object will refract through the lens and converge at the focal point on the other side of the lens. Convex lenses are “converging lenses”. Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

Formulas f = focal length do = object distance di = image distance hi = image height ho = object height M = magnification

Interpreting Calculations Focal length (f) convex or converging lens, f = + concave or diverging lens, f = - Image distance (di) di=+ , image is real & on opposite side of object di= -, image is virtual & on same side as object Magnification (M) M & hi = +, image is upright and virtual M & hi = - , image is inverted and real

Image is real & inverted Ray Diagram Convex Lens (do>f) – primary f on opposite side of lens Draw 2 - 3 rays from tip of object: 1) parallel, then through primary f 2) through the center of the lens 3) through f ‘(same side), then parallel 4) Image is located where the refracted rays converge Image is real & inverted object f image f ’

Convex Lens (Inside f)- primary f on opposite side Draw 2-3 rays from tip of object: 1) parallel, then through primary f 2) through the center of the lens 3) from f ‘on same side through tip of the object, then parallel 4) Extend the refracted rays back (dashed lines) to locate the image Ray Diagram Convex Lens (Inside f)- primary f on opposite side image Image is virtual, Upright, & larger f f ‘ object

Concave Lens – primary f on same side Ray Diagram Concave Lens – primary f on same side Draw 2-3 rays from tip of object & refract at vertical line: 1) parallel, then refracted ray from f on same side of lens 2) through the center of lens 3) Toward f ‘ on the other side of lens, then parallel 4) Extend refracted rays back (dashed lines) to locate image concave lens (axis) object image f f’ Image is virtual, upright, & smaller

Polarizing filters Only allows light to pass through in one plane Light is reduced by one-half Sunglasses – polarized vertically, cuts out the horizontal components of light to reduce glare from horizontal surfaces such as sand or water

Photoelectric Effect When light of certain frequencies shine on a surface, electrons are emitted from the surface. Accounted for by the photon or particle theory of light. Many applications such solar panels, photomultiplier tubes (or PMTs used in high energy physics to study particle collisions), and photocells (which operate switches or relays for automatic door openers and burgular alarms).