Light of wavelength passes though two slits separated by and is observed on a screen behind the slits. The location of the central maximum is marked on the screen and labeled
a. At what distance, on either side of , are the bright fringes?
b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?
c. With the glass in place, what is the phase difference between the two waves as they leave the slits?
d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?
(a) The distance of side is
(b) The fraction of the period of light wave is
(c) The phase between two waves is
(d) The central maximum move
We use the formula to location of the initial maximum, and we discover that
(b) Keep in mind that the time of a wave with a speed of and a frequency of is . As a result, the ratio we're after is
In terms of numbers, we have
The aspect difference is simply our result amplified by
In terms of numbers, we have
The axis will be shifted so that the time it takes for the light from the two slits to reach it is the same for each. Because one of the laser sources will arrive later, the new base must be placed near to the slit with the glass.
Consider the two right triangles generated by the light beam when there is no glass (the hypotenuses are denoted by ) and when the glass is added (the hypotenuses are denoted by . It is clear that if we regard to be the quickest distance,
We may also infer from the Euclidean theorem that by examining this right triangle,
As a conclusion, our unknown will be
Lastly, it should be self-evident.
When we combine these, we obtain
Note that while we can give this statement in terms we know, it is much easier to calculate and then insert the values used in the aforementioned formula.
The pinhole camera of FIGURE images distant objects by allowing only a narrow bundle of light rays to pass through the hole and strike the film. If light consisted of particles, you could make the image sharper and sharper (at the expense of getting dimmer and dimmer) by making the aperture smaller and smaller. In practice, diffraction of light by the circular aperture limits the maximum sharpness that can be obtained. Consider two distant points of light, such as two distant streetlights. Each will produce a circular diffraction pattern on the film. The two images can just barely be resolved if the central maximum of one image falls on the first dark fringe of the other image. (This is called Rayleigh’s criterion, and we will explore its implication for optical instruments in Chapter .)
a. Optimum sharpness of one image occurs when the diameter of the central maximum equals the diameter of the pinhole. What is the optimum hole size for a pinhole camera in which the film is behind the hole? Assume an average value for visible light.
b. For this hole size, what is the angle a (in degrees) between two distant sources that can barely be resolved?
c. What is the distance between two street lights away that can barely be resolved?
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 student performing a double-slit experiment is using a green laser with a wavelength of . She is confused when the maximum does not appear. She had predicted that this bright fringe would be from the central maximum on a screen behind the slits.
a. Explain what prevented the fifth maximum from being observed.
b. What is the width of her slits?
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