Interference effects are produced at point P on a screen as a result of direct rays from a 500-nm source and reflected rays off a mirror, as in Figure P24.59. If the source is 100 m to the left of the screen and 1.00 cm above the mirror, find the distance y (in millimeters) to the first dark band above the mirror.

A thin layer of oil floats on a puddle of water. When sunlight hits the film from directly above, the colors red (650 nm) and violet (390 nm) are reflected. What is the minimum thickness of the oil? Use n=1.5 for the oil, and n=1.33 for water.

A multi-mode fiber optic has a core index of n = 1.492 and a cladding index of 1.489. The diameter of the core is 30.0 microns. Monochromatic light is focused into one end of a perfectly straight fiber which is 25.0 km long. What will be the difference in arrival time at the far end of the fiber for the axial and marginal rays?

A glass sheet measuring 15.0 cmcm ×× 29.0 cmcm is covered by a very thin opaque coating. In the middle of this sheet is a thin, straight scratch 0.00125 mmmm thick, as shown in (Figure 1). The sheet is totally immersed beneath the surface of a liquid having an index of refraction of 1.41. Monochromatic light strikes the sheet perpendicular to its surface and passes through the scratch. A screen is placed under the liquid a distance 32.0 cmcm away from the sheet and parallel to it. You observe that the first dark fringes on either side of the central bright fringe on this screen are 23.0 cmcm apart. What is the wavelength of the light in air? Express your answer in nanometers.

A diffraction grating with n = 2.5E-05 lines/nm is used to separate two colors of light. The angle between their first maxima is Δθ ≡ θ1 - θ2 = 0.44 degrees, and the first light has wavelength λ1 = 618 nm.  Part (a)  Find θ1 using n and λ1 in radians.   Part (b)  Find θ2 in radians.  Part (c)  Find the value of the wavelength of the second color λ2 in nm.

A lens with an index of refraction of 1.60 is to be coated with a material (n = 1.40) that will make the lens nonreflecting for yellow-orange light (λλ = 515 nm) normally incident on the lens. What is the minimum required thickness of the coating?