# 0.4 2d and 3d wavefronts  (Page 5/7)

 Page 5 / 7

A slit with a width of 2511 nm has green light of wavelength 532 nm impinge on it. The diffracted light interferers on a surface, at what angle will the first minimum be?

1. We know that we are dealing with interference patterns from the diffraction of light passing through a slit. The slit has a width of 2511 nm which is $2511×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ and we know that the wavelength of the light is 532 nm which is $532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ . We are looking to determine the angle to first minimum so we know that $m=1$ .

2. We know that there is a relationship between the slit width, wavelength and interference minimum angles:

$sin\theta =\frac{m\lambda }{a}$

We can use this relationship to find the angle to the minimum by substituting what we know and solving for the angle.

3. $\begin{array}{ccc}\hfill sin\theta & =& \frac{532×{10}^{-9}\mathrm{m}}{2511×{10}^{-9}\mathrm{m}}\hfill \\ \hfill sin\theta & =& \frac{532}{2511}\hfill \\ \hfill sin\theta & =& 0.211867782\hfill \\ \hfill \theta & =& {sin}^{-1}0.211867782\hfill \\ \hfill \theta & =& 12.{2}^{o}\hfill \end{array}$

The first minimum is at 12.2 degrees from the centre peak.

From the formula $sin\theta =\frac{m\lambda }{a}$ you can see that a smaller wavelength for the same slit results in a smaller angle to the interference minimum. This is something you just saw in the two worked examples. Do a sanity check, go back and see if the answer makes sense. Ask yourself which light had the longer wavelength, which light had the larger angle and what do you expect for longer wavelengths from the formula.

A slit has a width which is unknown and has green light of wavelength 532 nm impinge on it. The diffracted light interferers on a surface, and the first minimum is measure at an angle of 20.77 degrees?

1. We know that we are dealing with interference patterns from the diffraction of light passing through a slit. We know that the wavelength of the light is 532 nm which is $532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ . We know the angle to first minimum so we know that $m=1$ and $\theta =20.{77}^{\mathrm{o}}$ .

2. We know that there is a relationship between the slit width, wavelength and interference minimum angles:

$sin\theta =\frac{m\lambda }{a}$

We can use this relationship to find the width by substituting what we know and solving for the width.

3. $\begin{array}{ccc}\hfill sin\theta & =& \frac{532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}}{a}\hfill \\ \hfill sin20.{77}^{o}& =& \frac{532×{10}^{-9}}{a}\hfill \\ \hfill a& =& \frac{532×{10}^{-9}}{0.354666667}\hfill \\ \hfill a& =& 1500×{10}^{-9}\hfill \\ \hfill a& =& 1500\phantom{\rule{4pt}{0ex}}\mathrm{nm}\hfill \end{array}$

The slit width is 1500 nm.

run demo

## Shock waves and sonic booms

Now we know that the waves move away from the source at the speed of sound. What happens if the source moves at the same time as emitting sounds? Once a sound wave has been emitted it is no longer connected to the source so if the source moves it doesn't change the way the sound wave is propagating through the medium. This means a source can actually catch up to the sound waves it has emitted.

The speed of sound is very fast in air, about $340\phantom{\rule{4pt}{0ex}}{\mathrm{m}·\mathrm{s}}^{-1}$ , so if we want to talk about a source catching up to sound waves then the source has to be able to move very fast. A good source of sound waves to discuss is a jet aircraft. Fighter jets can move very fast and they are very noisy so they are a good source of sound for our discussion. Here are the speeds for a selection of aircraft that can fly faster than the speed of sound.

 Aircraft speed at altitude ( ${\mathrm{km}·\mathrm{h}}^{-1}$ ) speed at altitude ( ${\mathrm{m}·\mathrm{s}}^{-1}$ ) Concorde 2 330 647 Gripen 2 410 669 Mirage F1 2 573 715 Mig 27 1 885 524 F 15 2 660 739 F 16 2 414 671

what is nutrients
what are the types of skeleton
endo skeleton and exo skeleton
Faith
or types of skeletons There is exo skeleton found in class insecta Exo skeleton found in phylum chordata and lastly hydrostatic skeleton found mainly in earth worms
Daniel
and hydrostatic skeleton
Godbless
what is life?
life is when any living thing breath or respirate.
Lucky
I want to join
Patrick
me too
Favour
me two
Monday
me too
Bengazy
me too
Maggie
I here
Yahaya
Does anybody knows another biology app that brings good understand
Lucky
give an example of a phylum where all members have open circulatory
anthropoda
Daniel
phylum Anthropoda
Daniel
how do u change the unit of temperature from degree celsius to degree Fahrenheit
Maggie
what are beneficial effects in industrial
create employment
ibrahim
provide food
ibrahim
pollution
ibrahim
dirty the environment
ibrahim
pollution and lack of knowledge about how to manage waste
Alex
what is gametophyte
what is biology
Biology deals with the study of living organisms and their interactions with each other and the environment.
Quartey
biology simply means the study of living and non-livingthings.
Shamstar
what is the meaning of ubiquitous
Under what topic is this question
fred
three branches of biology
what is the cell
what is life
Olajide
cell is the functional and structural unit of life
Shweta
life is a problem solving entity
Atanga
what is the characteristics of plant cell
Quaku
Describe the process that results in the formation of a tetrad.
what is biology
biology is the study of life
Oghenemine
what is biology
the study of life
Hamziyatu
what is the Biosphere?
I want to know what classifications of living organisms and their names
Quaku
are classified into plants and animals eukaryotic and prokaryotic cell.
Lokwe
what is biology?
what is the meaning of Biologists
Turabi
what is the meaning of Biologists
Turabi
what is the meaning of Biologists
Turabi
are those who are specialized in Biology
Nicode
Is the study of living things,
Kabel
what is the ecosystem?
Kabel
bio mean life logus means study so the study of living things or living organisms is called biology
Faraq
Ecosystem consists of the living organisms in a particular area together with the abiotic factors.
Quartey
Got questions? Join the online conversation and get instant answers! By    By  By  By 