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, θ 2, 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 n 1 sin θ 1 = n 2 sin θ 2 θ 1 is the angle of incidence 30.0° in this diagram θ 2 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