Refraction and Lenses

Refraction A wave is refracted when it “bends” in response to a change in speed. Moving across a boundary from one medium into another causes a change in the wavelength with a corresponding shift in direction.

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!

Refraction 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) Air (n = 1.00) Glass (n=1.50)

Relationship between angle, velocity, wavelength and index When the velocity changes it is the wavelength that changes, not the frequency These ratios relate the various characteristics of waves moving between media.

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

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) Only possible when light speeds up as it passes through the boundary n=1 r=900 n=1.5 c

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 medium according to the Law of Reflection (angle of incidence = angle of reflection) Application – fiber optic cables

Dispersion and Prisms The index of refraction depends on the wavelength of light so different colors of light bend at different angles. Shorter wavelengths (blue end of the visible spectrum) bend the most. A prism separates or disperses white light into the color spectrum as shown above.

Wavelength and Frequency of the visible light spectrum

Concave Lenses Thicker at the edges than in the center 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).

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

Sign conventions Focal length (f) Converging (convex) f = + Diverging (concave)  f = - Image distance (di) di=+ , image is real & on opposite side do= - , then image is virtual & on same side Magnification (M) M = +, image is erect & hi = + M = - , image is inverted & hi = -

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

Ray Diagram Convex Lens (Inside f) Image is virtual, erect, & larger 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) image Image is virtual, erect, & larger f f ‘ object

Ray Diagram Concave Lens Image is virtual, erect, & smaller 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) to lens along a line that would pass through 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, erect, & smaller

Polarizing filters Only allows light in one plane to pass through 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 The emission of electrons from a surface when light of certain frequencies shine on the surface.