Problems

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of $30.0\text{°}$?

Calculate the wavelength of light that has its third minimum at an angle of $30.0\text{°}$ when falling on double slits separated by $3.00\mu \text{m}$. Explicitly show how you follow the steps from the Problem-Solving Strategy: Wave Optics, located at the end of the chapter.

At what angle is the second-order maximum for the situation in the preceding problem?

Find the largest wavelength of light falling on double slits separated by $1.20\mu \text{m}$ for which there is a first-order maximum. Is this in the visible part of the spectrum?

(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

Shown below is a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, numerous bright spots appear, called fringes. Show that, for small angles (where $\text{sin}\theta \approx \theta$, with $\theta$ in radians), the distance between fringes is given by $\text{Δ}y=x\lambda \text{/}d$

Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm.

The source in Young’s experiment emits at two wavelengths. On the viewing screen, the fourth maximum for one wavelength is located at the same spot as the fifth maximum for the other wavelength. What is the ratio of the two wavelengths?

Red light of wavelength of 700 nm falls on a double slit separated by 400 nm. (a) At what angle is the first-order maximum in the diffraction pattern? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

The width of bright fringes can be calculated as the separation between the two adjacent dark fringes on either side. Find the angular widths of the third- and fourth-order bright fringes from the preceding problem.

What is the angular width of the central fringe of the interference pattern of (a) 20 slits separated by $d=2.0\times {10}^{\mathrm{-3}}\text{mm}$? (b) 50 slits with the same separation? Assume that $\lambda =600\text{nm}$.

An oil slick on water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?

Find the minimum thickness of a soap bubble that appears red when illuminated by white light perpendicular to its surface. Take the wavelength to be 680 nm, and assume the same index of refraction as water.

What are the three smallest non-zero thicknesses of soapy water ($n=1.33$) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light?

(a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of refraction as water. (b) Discuss the fragility of the film considering the thickness found.

A Michelson interferometer has two equal arms. A mercury light of wavelength 546 nm is used for the interferometer and stable fringes are found. One of the arms is moved by $1.5\mu \text{m}$. How many fringes will cross the observing field?

When the traveling mirror of a Michelson interferometer is moved $2.40\times {10}^{\mathrm{-5}}\text{m}$, 90 fringes pass by a point on the observation screen. What is the wavelength of the light used?

A chamber 5.0 cm long with flat, parallel windows at the ends is placed in one arm of a Michelson interferometer (see below). The light used has a wavelength of 500 nm in a vacuum. While all the air is being pumped out of the chamber, 29 fringes pass by a point on the observation screen. What is the refractive index of the air?