Refraction and Lenses

Refraction of Light As light travels from one media to another it bends. The path of light is bent as it crosses the boundary between two media due to refraction. The amount of refraction depends on properties of the two media and on the angle at which the light strikes the boundary. The straw appears to be broken at each boundary, but more so at air boundaries.

Snell’s Law of Refraction Snell’s Law of Refraction n1 sin q1 = n2 sin q2 The product of the index of refraction of the first medium and the sine of the angle of incidence is equal to the product of the index of refraction of the second medium and the sine of the angle of refraction.

The angle q is always measured from the normal. Indices of Refraction The index of refraction n depends on the material. When n1 < n2 sin q1 > sin q2 When n1 > n2 sin q1 < sin q2 The angle q is always measured from the normal.

Total Internal Refraction Index of Refraction n = c vmedium The index of refraction of a medium is equal to the speed of light in a vacuum divided by the speed of light in the medium.

Total Internal Reflection Total internal reflection occurs when light traveling from a region of a higher index of refraction to a region of a lower index of refraction strikes the boundary at an angle greater than the critical angle such that all light reflects back into the region of the higher index of refraction.

Critical Angle for Total Internal Reflection sin qc = n2 n1 The sine of the critical angle is equal to the index of refraction of the refracting medium divided by the index of refraction of the incident medium. Note: Optical fibers are an important technical application of total internal reflection. Light traveling through the transparent fiber always hits the internal boundary of the optical fiber at an angle greater than the critical angle, so all of the light is reflected and none of the light is transmitted through the boundary. Thus, the light maintains its intensity over the distance of the fiber.

Dispersion of Light White light separates into a spectrum of colors when it passes through a glass prism, this phenomenon is called dispersion. Note: Violet is refracted more than red because the speed of violet light through glass is less than the speed of red light through glass. Violet light has a higher frequency than red light, which causes it to interact differently with the atoms of the glass. This results in glass having a slightly higher index of refraction for violet light than it has for red light.

Dispersion of Light A prism is not the only means of dispersing light. A rainbow is a spectrum formed when sunlight is dispersed by water droplets in the atmosphere. Sunlight that falls on a water droplet is refracted. Because of dispersion, each color is refracted at a slightly different angle. At the back surface of the droplet, some of the light undergoes internal reflection. On the way out of the droplet, the light once again is refracted and dispersed.

Convex and Concave Lens A lens is a piece of transparent material, such as glass or plastic, that is used to focus light and form an image. Convex Lens - Converging Lens When surrounded by material with a lower index of refraction it refracts parallel light rays so that the rays meet at a point. Concave Lens – Diverging Lens When surrounded by material with a lower index of refraction rays passing through it spread out.

Thin Lens Equation and Magnification The inverse of the focal length of a spherical lens is equal to the sum of the inverses of the image position and the object position. Magnification The magnification of an object by a spherical lens, defined as the image height divided by the object height, is equal to the negative of the image position divided by the object position.

Properties of a Single Spherical Lens System NOTE: Virtual images are always on the same side of the lens as the object, which means that the image position is negative. A negative image height or magnification means the image is inverted compared to the object.

Convex Lenses and Real Images Paper can be ignited by producing a real image of the Sun on the paper. After being refracted by the lens, the rays converge at the focal point, F, of the lens. There are two focal points, one on each side of the lens. You could turn the lens around, and it will work the same.

Ray Diagrams If the object is placed at twice the focal length from the lens at the point 2F, the image also is found at 2F. Because of symmetry, the image and object have the same size. Thus, you can conclude that if an object is more than twice the focal length from the lens, the image is smaller than the object. If the object is between F and 2F, then the image is larger than the object.

Convex Lenses and Virtual Images When an object is placed at the focal point of a convex lens, the refracted rays will emerge in a parallel beam and no image will be seen. When the object is brought closer to the lens, the rays will diverge on the opposite side of the lens, and the rays will appear to an observer to come from a spot on the same side of the lens as the object. This is a virtual image that is upright and larger compared to the object.

Concave Lenses All images are virtual Focal length is negative (-) Image distance is negative (-) Object distance is positive (+)

Applications of Lenses The eyes of many people do not focus sharp images on the retina. Instead, images are focused either in front of the retina or behind it. External lenses, in the form of eyeglasses or contact lenses, are needed to adjust the focal length and move images to the retina. A nearsighted (myopia) person cannot see distant objects clearly because images are focused in front of the retina. The focal length of the eye is too short to focus the image on the retina. A concave lens corrects this defect. A farsighted (hyperopia) person cannot see close objects clearly because images are focused behind the retina. The focal length of the eye is too long. A convex lens corrects this defect.