Young’s double slit experiment gave definitive proof of the wave character of light.
An interference pattern is obtained by the superposition of light from two slits.
There is constructive interference when
$d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda}\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=\mathrm{0,}\phantom{\rule{0.25em}{0ex}}\mathrm{1,}\phantom{\rule{0.25em}{0ex}}-\mathrm{1,}\phantom{\rule{0.25em}{0ex}}\mathrm{2,}\phantom{\rule{0.25em}{0ex}}-\mathrm{2,}\phantom{\rule{0.25em}{0ex}}\dots )$ , where
$d$ is the distance between the slits,
$\theta $ is the angle relative to the incident direction, and
$m$ is the order of the interference.
There is destructive interference when
$d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\left(m+\frac{1}{2}\right)\lambda \phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.5em}{0ex}}m=\mathrm{0,}\phantom{\rule{0.25em}{0ex}}\mathrm{1,}\phantom{\rule{0.25em}{0ex}}-\mathrm{1,}\phantom{\rule{0.25em}{0ex}}\mathrm{2,}\phantom{\rule{0.25em}{0ex}}-\mathrm{2,}\phantom{\rule{0.25em}{0ex}}\dots )$ .
Conceptual questions
Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.
Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.
[link] shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.
Calculate the wavelength of light that has its third minimum at an angle of
$\text{30}\text{.}\mathrm{0\xba}$ when falling on double slits separated by
$3\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{\mu m}$ . Explicitly, show how you follow the steps in
Problem-Solving Strategies for Wave Optics .
What is the wavelength of light falling on double slits separated by
$2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{\mu m}$ if the third-order maximum is at an angle of
$\text{60}\text{.}\mathrm{0\xba}$ ?
Find the largest wavelength of light falling on double slits separated by
$1\text{.}\text{20}\phantom{\rule{0.25em}{0ex}}\text{\mu m}$ for which there is a first-order maximum. Is this in the visible part of the spectrum?
(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of
$\text{10}\text{.}\mathrm{0\xba}$ , at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?
[link] shows 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, there will be numerous bright spots, called fringes. Show that, for small angles (where
$\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta $ , with
$\theta $ in radians), the distance between fringes is given by
$\text{\Delta}y=\mathrm{x\lambda}/d$ .
For small angles
$\text{sin}\phantom{\rule{0.25em}{0ex}}\theta -\text{tan}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta \phantom{\rule{0.25em}{0ex}}(\text{in radians})$ .
Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in
[link] .
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 (see
[link] ).
A petrol engine has a output of 20 kilowatts and uses 4.5 kg of fuel for each hour of running. The energy given out when 1 kg of petrol is burnt is 4.8 × 10 to the power of 7 Joules.
a) What is the energy output of the engine every hour?
b) What is the energy input of the engine every hour?
A simple pendulum is used in a physics laboratory experiment to obtain an experimental value for the gravitational acceleration, g . A student measures the length of the pendulum to be 0.510 meters, displaces it 10 o from the equilibrium position, and releases it. Using a s
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed?
Reduce that two body problem into one body problem. Apply potential and k. E formula to get total energy of the system
rakesh
i dont think dere is any potential energy... by d virtue of no height present
Olalekan
there is compressed energy,dats only potential energy na?
rakesh
yes.. but... how will u approach that question without The Height in the question?
Olalekan
Can you explain how you get 54J?
Emmanuel
Because mine is 36J
Emmanuel
got 36J too
Douglas
OK the answer is 54J
Babar is correct
Emmanuel
Conservation of Momentum
Emmanuel
woow i see.. can you give the formula for this
joshua
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed? Asume there is no external force.
may be by using MC^2=MC^2 and Total energy=kinetic energy +potential energy
so 1st find kinetic energy and den find potential energy which is stored energy
we are given f=12 m=200g which is 0.2kg
now from 2nd law of newton a= f/m=60m/s*2
work done=force applied x displacement cos (theta)
w= 12x60 =720nm/s*2
Mudang
this very interesting question very complicated for me, í need urgent help.
1,two buses A and B travel along the same road in the same direction from Harper city (asume They both started from the same point) to Monrovia. if bus A maintains a Speedy of 60km/h and bus B a Speedy of 75km/h, how many
mohammed
hours Will it take bus B to overtake bus A assuming bus B starts One hour after bus A started. what is the distance travelled by the buses when They meet?.
mohammed
pls í need help
mohammed
4000 work is done
Ana
speed=distance /time
distance=speed/time
Ana
now use this formula
Ana
what's the answer then
Julius
great Mudang
Kossi
please Ana
explain 4000 ?
babar
hey mudang
there is a product of force and acceleration not force and displacement
babar
@Mohammed answer is 0.8hours or 48mins
Douglas
nice
A.d
its not possible
Olalekan
í want the working procedure
mohammed
the answer is given but how Will One arrive at it. the answers are 4hours and 300m.
mohammed
physics is the science that studies the non living nature
For first equation simply integrate formula of acceleration in the limit v and u
Tripti
For second itegrate velocity formula by ising first equation
Tripti
similarly for 3 one integrate acceleration again by multiplying and dividing term ds
Tripti
any methods can take to solve this eqtions
a=vf-vi/t
vf-vi=at
vf=vi+at......1
Ana
suppose a body starts with an initial velocity vi and travels with uniform acceleration a for a period of time t.the distance covered by a body in this time is "s" and its final velocity becomes vf
Ana
what is the question dear
Zeeshan
average velocity=(vi+vf)/2
distance travelled=average velocity ×time
therefore s=vi+vf/2×t
from the first equation of motion ,we have
vf =vi+at
s=[vi+(vi+at)]/2×t
s=(2vi+at)/2×t
s=bit+1/2at2
Ana
find the distance
Ana
how
Zeeshan
Two speakers are arranged so that sound waves with the same frequency are produced and radiated through a room. An interference pattern is created. Calculate the distance between the two speakers?