Chapter 35: Q35P (page 1076)
We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this?
The minimum thickness of coating is
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray (the light does not reflect inside material 2) and (the light reflects twice inside material 2). The waves of andinterfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction and the type of interference, the thin-layer thickness in nanometers, and the wavelength in nanometers of the light as measured in air. Where is missing, give the wavelength that is in the visible range. Where is missing, give the second least thickness or the third least thickness as indicated.
White light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are for the top material, for the thin film, and for the bottom material. The film thickness is . Of the visible wavelengths ( to ) that result in fully constructive interference at an observer above the film, which is the (a) longer and (b) shorter wavelength? The materials and film are then heated so that the film thickness increases. (c) Does the light resulting in fully constructive interference shift toward longer or shorter wavelengths?
In Fig. 35-4, assume that the two light waves, of wavelength in air, are initially out of phase by rad. The indexes of refraction of the media are and . What are the (a) smallest and (b) second smallest value of that will put the waves exactly in phase once they pass through the two media?
If you move from one bright fringe in a two-slit interference pattern to the next one farther out,
(a) does the path length difference increase or decrease and
(b) by how much does it change, in wavelengths ?
A Newton’s rings apparatus is to be used to determine the radius of curvature of a lens . The radii of the nth and bright rings are found to be and , respectively, in light of wavelength . Calculate the radius of curvature of the lower surface of the lens.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
