A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is . A helium-neon laser is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating.
a. What is the first-order diffraction angle of the laser beam?
b. What is the first-order diffraction angle of the laser beam after the aquarium is filled with water ?
(a) The first order diffraction angle of the laser beam is
(b) The first-order diffraction angle of the laser beam after the aquarium is filled with water is
We must presume that the beam is horizontal to the tank walls.
The walls of the aqua, on the other hand, have no impact on the angle.
Let's also assume that lines per mm means that now the interval will be
The angle is measured by
Then our perspective will be
If we have freshwater, instead of , we will have , which will give us
Then our perspective will be substitute in
A helium-neon laser is built with a glass tube of inside diameter , as shown in FIGURE P33.62. One mirror is partially transmitting to allow the laser beam out. An electrical discharge in the tube causes it to glow like a neon light. From an optical perspective, the laser beam is a light wave that diffracts out through a -mm-diameter circular opening.
a. Can a laser beam be perfectly parallel, with no spreading? Why or why not?
b. The angle to the first minimum is called the divergence angle of a laser beam. What is the divergence angle of this laser beam?
c. What is the diameter (in mm) of the laser beam after it travels
d. What is the diameter of the laser beam after it travels ?
Helium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen behind the grating. The emission at wavelength creates a first-order bright fringe from the central maximum. What is the wavelength of the bright fringe that is from the central maximum?
Find an expression for the positions of the first-order fringes of a diffraction grating if the line spacing is large enough for the small-angle approximation to be valid. Your expression should be in terms of and .
. Use your expression from part a to find an expression for the separation on the screen of two fringes that differ in wavelength by . Rather than a viewing screen, modern spectrometers use detectors-similar to the one in your digital camera-that are divided into pixels. Consider a spectrometer with a grating and a detector with located behind the grating. The resolution of a spectrometer is the smallest wavelength separation that can be measured reliably. What is the resolution of this spectrometer for wavelengths near , in the center of the visible spectrum? You can assume that the fringe due to one specific wavelength is narrow enough to illuminate only one column of pixels.
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