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Optics

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The electromagnetic spectrum

Visible light make up only a small part of the entire spectrum ofelectromagnetic waves. Unlike sound waves and mechanical waves, they don’ t require a material medium for their transmission, they can propagate through a vacuum. Electromagnetic waves consist of time-varying electric and magnetic fields that propagate perpendicular to each other and to the direction of the propagation of the wave. All electromagnetic waves travel at a fixed speed through a vacuum

regardless of their frequency.

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Dispersion and Refraction

Prisms display the phenomena called dispersion by separating white light into components of different wavelength (different colors). The different colors refract at different angles, splitting white light into a rainbow. When light passes through a prism, it is refracted twice, when it enters the prism and when it leaves. Refraction is the change in direction of light as it leaves one medium and enters a different medium. Every medium has a characteristic value called the index of refraction which is a value used to give the ratio of the speed an electromagnetic wave in vacuum to the speed of the electromagnetic wave in a particular medium.

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RefractionRefraction is the slowing of light by matter and it follows Snell’s Law. It is the bending of any wave, such as a light or sound wave, when it passes from one medium into another of different optical density

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities in the two media or the ratio of the index of refraction for the two media.

or

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Snell’s Law

Normal

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ProblemIf a light beam makes an angle of 40º with the surface, it makes an angle of 50º with the normal; this is the angle of incidence. We can find the angle of refraction by using Snell’s Law.

Solution

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Magnification v is the distance from the lens to the image. u is the distance from the lens to the object. a is the height of the image, b is the height of the object.

Thin Lens Equationu is the distance (measured along the axis) from the image to the center of the lens The image is real, inverted, and behind the lens if u is positive. The image is virtual, upright, and in front of the lens if u is negative.

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The approximation for thin lenses

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The thin-lens diagam is composed of three rays:

Ray number 1.) A ray from the top of the object parallel to the centerline and perpendicular to the lends. It then travels through the focal point on the other side of the lens.Ray number 3.) A ray through the center of the lens which won't be bent. Ray number 2.) A ray through the focal ponit on the near side of the lens.

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ProblemAn object of height 14 cm is placed 46 cm in front of a converging lens with a focal length of 26 cm. Where is the image? Is it real or virtual? Is it upright or inverted? What’s the height of the image?With u = 46 cm and f = 26 cm, the lens equation gives us

Because v is positive. the image is real. Real images are inverted. The magnification is

The height of the image is given by

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Every point of a wave front can be considered the origin of a new circular or spherical wave, the so-called elemetary wave. The new position of the wave front results from the superposition of all of the elementary waves. The Huygens wave front is a series of concentric circles originating from the points on a wave front.

Huygen’s Principle

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Diffraction in a Single Slit

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If a wave front goes through a single slit, it breaks down into individual circular waves called elementary waves. As we know through Huygen’s Principle, the single slit acts a point source for a new circular or spherical wave. This phenomena is called diffraction.

The difference between refraction and diffractionIn refraction, the wave is being bent because the speed of propagation in the medium it is moving into is different than the medium it is moving out of. For instance, light moving from air to water at an angle is bent away from the axis that runs perpendicularly to the surface because light travels slower in water than in air.In diffraction, the wave is being bent (often times through very small slits) when it hits somthing, causing a diffraction pattern to form.

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Double Slit Interference

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Double Slit Interference

source

screen

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where is the wavelength of the light, d is the separation between the two slits and n is the order of maximum observed (central maximum is n = 0)

bright bands

dark bands

If the crests and troughs of the two waves arrive at the screen at the same time, then the waves interfere constructively and a bright band appears on the screen. If the crest of one wave arrives at the same time as the trough of the other wave, then the waves interfere destructively and cancel each other out. This area of the screen will be dark. If the distance to the screen D is much larger than the distance between the stripes, the conditions for bright or dark bands are

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Problem When sodium yellow light (¸ = 589 nm) is used in a double slit experiment, the first order maximum is 0.035 cm from the central maximum. When another light source of unknown wavelength is used. The first order maximum occurs at 0.03 cm from the center. What is this wavelength? and , thus