Refraction

As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.

Refraction of Light

Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.

The speed of all electromagnetic radiation in vacuum is the same, approximately 3×108 meters per second, and is denoted by c. Therefore, if v is the phase velocity of radiation of a specific frequency in a specific material, the refractive index is given by

INDEX OF REFRACTION

This number is typically greater than one: the higher the index of the material, the more the light is slowed down.

Because the Refractive Index for a given substance at a given temperature and pressure is a constant, Refractive Indices are used in the real world to determine everything from the percentage of water in a sample of honey to the composition and purity of gemstones.

Snell's law is used to calculate how much refraction occurs. This is determined from the refractive index (RI) and the angle of incidence (i). Rays move towards the normal whenthe ray slows downand away from the normal when the rayspeeds up

Image Formation

Total Internal Reflection When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle qc , and for incident angles greater than the critical angle there will be total internal reflection

The field of fiber optics depends upon the total internal reflection of light rays traveling through tiny optical fibers. The fibers are so small that once the light is introduced into the fiber with an angle within the confines of the numerical aperture of the fiber, it will continue to reflect off the walls of the fiber and thus can travel long distances in the fiber. Bundles of such fibers can accomplish imaging of otherwise inaccessible areas.

If a luminous object is placed at a distance greater than the focal length away from a convex lens, then it will form an inverted real image on the opposite side of the lens. The image position may be found from the lens equation or by using a ray diagram.

Real Image Formation

Virtual Image Formation

Refraction Rule for a Converging LensAny incident ray traveling parallel to the principal axis of a converging lens will

refract through the lens and travel through the focal point on the opposite side of the

lens.

Refraction Rules for a Converging LensAny incident ray traveling parallel to the principal axis of a

converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel

parallel to the principal axis.

Refraction Rule for a Diverging LensAny incident ray traveling parallel to the principal axis of a

diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension

will pass through the focal point).

Refraction Rules for a Diverging LensAny incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its

extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel

parallel to the principal axis.

Refraction Rules for a Converging LensAny incident ray traveling parallel to the principal axis of a

converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.

Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the

principal axis. An incident ray which passes through the center of the lens will

in affect continue in the same direction that it had when it entered the lens.

Refraction Rules for a Diverging LensAny incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its

extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel

parallel to the principal axis. An incident ray which passes through the center of the lens will in affect continue in the same direction that it

had when it entered the lens.

Ray Diagram for Object Located in Front of the Focal Point

Ray Diagram for Object Located at the Focal Point

Converging Lenses - Object-Image Relations

Step-by-Step Method for Drawing Ray Diagrams

Diverging Lenses - Object-Image Relations

The Mathematics of Lenses

Sign Conventions f is + if the lens is a double convex lens

(converging lens)

f is - if the lens is a double concave lens (diverging lens)

di is + if the image is a real image and located on the opposite side of the lens.

di is - if the image is a virtual image and located on the object's side of the lens.

hi is + if the image is an upright image (and therefore, also virtual)

hi is - if the image an inverted image (and therefore, also real)

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