Chapter 35

In your research lab, a very thin, flat piece of glass with refractive index 1.40 and uniform thickness covers the opening of a chamber that holds a gas sample. The refractive indexes of the gases on either side of the glass are very close to unity. To determine the thickness of the glass, you shine coherent light of wavelength ${\lambda }_0$ in vacuum at normal incidence onto the surface of the glass. When ${\lambda }_0$ = 496 nm, constructive interference occurs for light that is reflected at the two surfaces of the glass. You find that the next shorter wavelength in vacuum for which there is constructive interference is 386 nm. (a) Use these measurements to calculate the thickness of the glass. (b) What is the longest wavelength in vacuum for which there is constructive interference for the reflected light?

The index of refraction of a glass rod is 1.48 at $T$ =20.0${}^{\circ }$C and varies linearly with temperature, with a coefficient of 2.50 $\times$ 10${}^{-5}$/C${}^{\circ }$. The coefficient of linear expansion of the glass is 5.00 $\times$ 10${}^{-6}$/C${}^{\circ }$. At 20.0${}^{\circ }$C the length of the rod is 3.00 cm. A Michelson interferometer has this glass rod in one arm, and the rod is being heated so that its temperature increases at a rate of 5.00 C${}^{\circ }$/min. The light source has wavelength $\lambda$ = 589 nm, and the rod initially is at $T$ = 20.0${}^{\circ }$C. How many fringes cross the field of view each minute?