Refraction & Lenses

Refraction & Lenses

Refraction of Light • When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium • The ray that enters the second medium is bent at the boundary • This bending of the ray is called refraction

Refraction of Light, cont • The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane • The angle of refraction, θ2, depends on the properties of the medium

Following the Reflected and Refracted Rays • Ray  is the incident ray • Ray  is the reflected ray • Ray  is refracted into the lucite • Ray  is internally reflected in the lucite • Ray  is refracted as it enters the air from the lucite

More About Refraction • The angle of refraction depends upon the material and the angle of incidence • The path of the light through the refracting surface is reversible

Refraction Details, 1 • Light may refract into a material where its speed is lower • The angle of refraction is less than the angle of incidence • The ray bends toward the normal

Refraction Details, 2 • Light may refract into a material where its speed is higher • The angle of refraction is greater than the angle of incidence • The ray bends away from the normal

The Index of Refraction • When light passes from one medium to another, it is refracted because the speed of light is different in the two media • The index of refraction, n, of a medium can be defined

Index of Refraction, cont • For a vacuum, n = 1 • For other media, n > 1 • n is a unitless ratio

Some Indices of Refraction

Snell’s Law of Refraction • n1 sin θ1 = n2 sin θ2 • θ1 is the angle of incidence • 30.0° in this diagram • θ2 is the angle of refraction

Using Spectra to Identify Gases • All hot, low pressure gases emit their own characteristic spectra • The particular wavelengths emitted by a gas serve as “fingerprints” of that gas • Some uses of spectral analysis • Identification of molecules • Identification of elements in distant stars • Identification of minerals

The Rainbow • A ray of light strikes a drop of water in the atmosphere • It undergoes both reflection and refraction • First refraction at the front of the drop • Violet light will deviate the most • Red light will deviate the least

The Rainbow, 2 • At the back surface the light is reflected • It is refracted again as it returns to the front surface and moves into the air • The rays leave the drop at various angles • The angle between the white light and the violet ray is 40° • The angle between the white light and the red ray is 42°

Observing the Rainbow • If a raindrop high in the sky is observed, the red ray is seen • A drop lower in the sky would direct violet light to the observer • The other colors of the spectra lie in between the red and the violet

Total Internal Reflection • Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction • Ray 5 shows internal reflection

Critical Angle • A particular angle of incidence will result in an angle of refraction of 90° • This angle of incidence is called the critical angle

Critical Angle, cont • For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary • This ray obeys the Law of Reflection at the boundary • Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

Fiber Optics • An application of internal reflection • Plastic or glass rods are used to “pipe” light from one place to another • Applications include • medical use of fiber optic cables for diagnosis and correction of medical problems • Telecommunications

Thin Lenses • A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane • Lenses are commonly used to form images by refraction in optical instruments

Thin Lens Shapes • These are examples of converging lenses • They have positive focal lengths • They are thickest in the middle

More Thin Lens Shapes • These are examples of diverging lenses • They have negative focal lengths • They are thickest at the edges

Focal Length of Lenses • The focal length, ƒ, is the image distance that corresponds to an infinite object distance • This is the same as for mirrors • A thin lens has two focal points, corresponding to parallel rays from the left and from the right • A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible

Focal Length of a Converging Lens • The parallel rays pass through the lens and converge at the focal point • The parallel rays can come from the left or right of the lens

Focal Length of a Diverging Lens • The parallel rays diverge after passing through the diverging lens • The focal point is the point where the rays appear to have originated

Lens Equations • The geometric derivation of the equations is very similar to that of mirrors

Lens Equations • The equations can be used for both converging and diverging lenses • A converging lens has a positive focal length • A diverging lens has a negative focal length

Sign Conventions for Thin Lenses

Focal Length for a Lens • The focal length of a lens is related to the curvature of its front and back surfaces and the index of refraction of the material • This is called the lens maker’s equation

Ray Diagrams for Thin Lenses • Ray diagrams are essential for understanding the overall image formation • Three rays are drawn • The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths • The second ray is drawn through the center of the lens and continues in a straight line • The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis • There are an infinite number of rays, these are convenient

Ray Diagram for Converging Lens, p > f • The image is real • The image is inverted

Ray Diagram for Converging Lens, p < f • The image is virtual • The image is upright

Ray Diagram for Diverging Lens • The image is virtual • The image is upright

Spherical Aberration • Results from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axis • For a mirror, parabolic shapes can be used to correct for spherical aberration

Chromatic Aberration • Different wavelengths of light refracted by a lens focus at different points • Violet rays are refracted more than red rays • The focal length for red light is greater than the focal length for violet light • Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses

Refraction & Lenses