At the larger angle shown in part (c), the path lengths differ by
$3\text{\lambda}\text{/}2$ for rays from the top and bottom of the slit. One ray travels a distance
$\lambda $ different from the ray from the bottom and arrives in phase, interfering constructively. Two rays, each from slightly above those two, also add constructively. Most rays from the slit have another ray to interfere with constructively, and a maximum in intensity occurs at this angle. However, not all rays interfere constructively for this situation, so the maximum is not as intense as the central maximum. Finally, in part (d), the angle shown is large enough to produce a second minimum. As seen in the figure, the difference in path length for rays from either side of the slit is
D sin
$\theta $ , and we see that a destructive minimum is obtained when this distance is an integral multiple of the wavelength.
Thus, to obtain
destructive interference for a single slit ,
where
D is the slit width,
$\text{\lambda}$ is the light’s wavelength,
$\theta $ is the angle relative to the original direction of the light, and
m is the order of the minimum.
[link] shows a graph of intensity for single-slit interference, and it is apparent that the maxima on either side of the central maximum are much less intense and not as wide. This effect is explored in
Double-Slit Diffraction .
Calculating single-slit diffraction
Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of
$45.0\text{\xb0}$ relative to the incident direction of the light, as in
[link] . (a) What is the width of the slit? (b) At what angle is the first minimum produced?
Strategy
From the given information, and assuming the screen is far away from the slit, we can use the equation
$D\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =m\lambda $ first to find
D , and again to find the angle for the first minimum
${\theta}_{1}.$
Solution
We are given that
$\text{\lambda}=550\phantom{\rule{0.2em}{0ex}}\text{nm}$ ,
$m=2$ , and
${\theta}_{2}=45.0\text{\xb0}$ . Solving the equation
$D\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =m\lambda $ for
D and substituting known values gives
Solving the equation
$D\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =m\lambda $ for
$\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{1}$ and substituting the known values gives
We see that the slit is narrow (it is only a few times greater than the wavelength of light). This is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects such as this single-slit diffraction pattern. We also see that the central maximum extends
$20.7\text{\xb0}$ on either side of the original beam, for a width of about
$41\text{\xb0}$ . The angle between the first and second minima is only about
$24\text{\xb0}$$\left(45.0\text{\xb0}-20.7\text{\xb0}\right)$ . Thus, the second maximum is only about half as wide as the central maximum.
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine:
1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles.
2) in Genomic medicine
3) in protein folding
4) in radio theraphy(MRI)
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart. One explanation for dark energy is that it is a property of space.