91Ó°ÊÓ

A double slit is illuminated simultaneously with orange light of wavelength $620\mathrm{nm}$ and light of an unknown wavelength. The $\mathrm{m}=4$ bright fringe of the unknown wavelength overlaps the $\mathrm{m}=3$ bright orange fringe. What is the unknown wavelength$?$

FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.

Light of wavelength$620\mathrm{nm}$illuminates a diffraction grating. The second-order maximum is at angle $39.5°$. How many lines per millimeter does this grating have?

A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure) using light of wavelength l. If the wavelength is changed to $\mathrm{λ}/2$, does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.

A diffraction grating produces a first-order maximum at an angle of $20.0°$. What is the angle of the second-order maximum?

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are $656\mathrm{nm}$ (red) and $486\mathrm{nm}$ (blue). Light from a hydrogen lamp illuminates a diffraction grating with $500\mathrm{lines}/\mathrm{mm}$, and the light is observed on a screen $1.50\mathrm{m}$ behind the grating. What is the distance between the first-order red and blue fringes?

A helium-neon laser $(\mathrm{λ}=633\mathrm{nm})$ illuminates a diffraction grating. The distance between the two $\mathrm{m}=1$ bright fringes is $32\mathrm{cm}$ on a screen $2.0\mathrm{m}$ behind the grating. What is the spacing between slits of the grating$?$

In a single-slit experiment, the slit width is $200$ times the wavelength of the light. What is the width $(\mathrm{in}\mathrm{mm})$of the central maximum on a screen $2.0\mathrm{m}$ behind the slit$?$

Light of$630\mathrm{nm}$wavelength illuminates a single slit of width $0.15\mathrm{mm}$. FIGURE $\mathrm{EX}33.17$shows the intensity pattern seen on a screen behind the slit. What is the distance to the screen$?$

You need to use your cell phone, which broadcasts an $800\mathrm{MHz}$signal, but you're behind two massive, radio-wave absorbing buildings that have only a$15\mathrm{m}$space between them. What is the angular width, in degrees, of the electromagnetic wave after it emerges from between the buildings$?$