General Physics II Ray Optics 1
Dispersion White light is a combination of all the wavelengths of the visible part of the electromagnetic spectrum. Red light has the longest wavelengths and violet light the shortest. The speed of light in vacuum is the same for all wavelengths. However, in a material medium, the speed depends on the wavelength and hence the index of refraction depends on the wavelength. This is called dispersion. For most common transparent materials, the index of refraction is greatest for violet light (smallest λ) and smallest for red (greatest λ). Hence, violet light travels slowest and red fastest in these media. deepest violet deepest red 2
Dispersion When white light enters such a medium at a non-zero angle of incidence from air, because the index of refraction is different for each wavelength, each wavelength will be refracted at a (slightly) different angle. This causes the different wavelength components to separate into a band of color. Because the index of refraction increases from red to violet, red is deviated the least from the incident direction and violet the most. When a prism is used, a second refraction as the light exits the prism enhances the spreading. This enhancement is due to the fact that the normals to the two refracting surfaces are in different directions. A rainbow is formed by dispersion produced by raindrops. 3
Dispersion 4
Rainbows 5
For the primary rainbow, which raindrops are highest in the sky? 1. The drops from which we see red. 2. The drops from which we see violet. 3. Neither of the above. All the drops producing the rainbow are at the same height. 6
Images Formed by a Single Refracting Surface An object below the surface of a pool of water seems to be closer to the surface than it actually is, when viewed from above the surface. (We are assuming that air, which has the smaller refractive index, is above the surface of the water.) This phenomenon is due to the refraction of light rays at the air-water interface. 7 7
Images Formed by a Single Refracting Surface For rays that are close to the optical axis, one finds that the object distance (s) and the image distance (s ) are related by n s = 2 n s. 1 n 1 is the index of refraction of the medium in which the object is located and n 2 is the index of refraction of the medium in which the observer is located. 8
Workbook: Chapter 18, Question 17 9
A thin lens is one whose thickness is very small compared with the radii of curvature of the curved surfaces of the lens. A converging lens is one that causes rays parallel to the optical axis of the lens to converge to a point after passing through the lens. This point of convergence is called the focal point. There is one focal point on either side of the lens. The focal length is the distance from the center of the lens to a focal point. Thin Lenses 10
How a Converging Lens Works Note: n for the lens is greater than n for the medium outside. 11
If a beam of white light falls on a converging lens made of ordinary glass, the red portion of the light will be focused 1. Closer to the lens than the blue portion 2. Farther from the lens than the blue 3. At the same point as the blue 12
A diverging lens is one that causes rays parallel to the optic axis of the lens to diverge after passing through the lens. The diverging rays appear to originate from a single point the focal point. As with a converging lens, there is one focal point on either side of the lens. Diverging Lenses 13
How a Diverging Lens Works Note: n for the lens is greater than n for the medium outside. 14
Image Formation by Thin Lenses: Ray Tracing In the figure above, a real image of the object is formed by the converging lens. The image is real because light rays from each point on the object, after refraction by the lens, converge to a corresponding point on the image. The image will be formed on a screen placed at its location. 15
Image Formation by Thin Lenses: Ray Tracing Three principal rays diverging from a point on the object are used to determine the position, size, and orientation of the image of this point formed by a thin lens. 1. A ray initially parallel to the optical axis emerges from the lens in a direction that takes it through the far focal point of a converging lens. For a diverging lens, the outgoing ray appears to originate from the first focal point of a lens. 2. A ray that passes through the center of the lens is essentially undeviated. 3. A ray that passes through the near focal point of a converging lens emerges parallel to the optical axis. A ray traveling toward the far focal point of a diverging lens emerges parallel to the axis. Drawing any two of these rays is sufficient to determine the position, size, and orientation of the image. 16
Image Formation by Thin Lenses: Ray Tracing Converging Lenses h h Magnification = h. h 17
Image Formation by Thin Lenses: Ray Tracing 18
Workbook: Chapter 18, Question 22 19
Image Formation by Thin Lenses: Ray Tracing Diverging Lenses The image formed by a single diverging lens is always virtual, upright, and reduced in size compared to the object 20
Workbook: Chapter 18, Question 23 21