1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vazorg [7]
3 years ago
6

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed o

n a screen that is 2.30m from the grating.In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 2.98 mm. What is the difference between these wavelengths?
Physics
1 answer:
kobusy [5.1K]3 years ago
3 0

Answer:

\Delta \lambda=14.3\ nm

Explanation:

It is given that,

The number of lines per unit length, N = 900 slits per cm

Distance between the formed pattern and the grating, l = 2.3 m

n the first-order spectrum, maxima for two different wavelengths are separated on the screen by 2.98 mm, \Delta Y=2.98\ mm = 0.00298\ m

Let d is the slit width of the grating,

d=\dfrac{1}{N}

d=\dfrac{1}{900\ cm}

d=1.11\times 10^{-5}\ m

For the first wavelength, the position of maxima is given by :

y_1=\dfrac{L\lambda_1}{d}

For the other wavelength, the position of maxima is given by :

y_2=\dfrac{L\lambda_2}{d}

So,

\Delta \lambda=\dfrac{\Delta y d}{l}

\Delta \lambda=\dfrac{0.00298\times 1.11\times 10^{-5}}{2.3}

\Delta \lambda=1.43\times 10^{-8}\ m

or

\Delta \lambda=14.3\ nm

So, the difference between these wavelengths is 14.3 nm. Hence, this is the required solution.

You might be interested in
A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. Use the vertical motio
Gnoma [55]

Answer:

3.25 seconds

Explanation:

It is given that,

A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. The equation for his motion is as follows :

h=-16t^2+vt+s

Where

s is the height in feet

For the given condition, the equation becomes:

h=-16t^2+50t+7

When it hits the ground, h = 0

i.e.

-16t^2+50t+7=0

It is a quadratic equation, we find the value of t,

t = 3.25 seconds and t = -0.134 s

Neglecting negative value

Hence, for 3.25 seconds the baseball is in the air before it hits the ground.

6 0
3 years ago
Read 2 more answers
the two forces f1 and f2 acting at A have a resultant force of Fr= -100lb. determine the magnitude and coordinate direction angl
faust18 [17]
Two forces F<span>1 and </span>F<span>2 act on the screw eye. The resultant force </span>FR<span> has a magnitude of 125 lb and the coordinate direction angles shown in (Figure 1) . Determine the magnitude of </span>F<span>2. Determine the coordinate direction angle </span>α<span>2 of </span>F<span>2. Determine the coordinate direction angle </span>β<span>2 of </span>F<span>2. Determine the coordinate direction angle </span>γ<span>2 of </span>F<span>2.</span>
8 0
3 years ago
An Olympic discus thrower (~100 kg) launches the 2.0 kg discus by spinning rapidly (~4 times per second) with arm outstretched (
vladimir1956 [14]

Answer:

F = 1263.03 N

Explanation:s

given,                      

mass of the disk thrower = 100 Kg

mass of the disk = 2 Kg                

angular speed of the disk  = 4 rev/s

arm outstretched = 1 m                  

centripetal force of the disk in the circular path

F = m ω² r                        

ω = 4 x 2 x π        

ω = 25.13 rad/s

F = m ω² r                      

F = 2 x 25.13² x 1

F = 1263.03 N                                              

hence, centripetal force equal to the F = 1263.03 N

6 0
3 years ago
A spherical capacitor contains a charge of 3.00 nC when connected to a potential difference of 230 V. If its plates are separate
Assoli18 [71]

Answer:

Part(a): the capacitance is 0.013 nF.

Part(b): the radius of the inner sphere is 3.1 cm.

Part(c): the electric field just outside the surface of inner sphere is \bf{2.81 \times 10^{4}~n~C^{-1}}.

Explanation:

We know that if 'a' and 'b' are the inner and outer radii of the shell respectively, 'Q' is the total charge contains by the capacitor subjected to a potential difference of 'V' and '\epsilon_{0}' be the permittivity of free space, then the capacitance (C) of the spherical shell can be written as

C = \dfrac{4 \pi \epsilon_{0}}{(\dfrac{1}{a} - \dfrac{1}{b})}~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)

Part(a):

Given, charge contained by the capacitor Q = 3.00 nC and potential to which it is subjected to is V = 230V.

So the capacitance (C) of the shell is

C &=& \dfrac{Q}{V} = \dfrac{3 \times 10^{-90}~C}{230~V} = 1.3 \times 10^{-11}~F = 0.013~nF

Part(b):

Given the inner radius of the outer shell b = 4.3 cm = 0.043 m. Therefore, from equation (1), rearranging the terms,

&& \dfrac{1}{a} = \dfrac{1}{b} + \dfrac{1}{C/4 \pi \epsilon_{0}} = \dfrac{1}{0.043} + \dfrac{1}{1.3 \times 10^{-11} \times 9 \times 10^{9}} = 31.79\\&or,& a = \dfrac{1}{31.79}~m = 0.031~m = 3.1~cm

Part(c):

If we apply Gauss' law of electrostatics, then

&& E~4 \pi a^{2} = \dfrac{Q}{\epsilon_{0}}\\&or,& E = \dfrac{Q}{4 \pi \epsilon_{0}a^{2}}\\&or,& E = \dfrac{3 \times 10^{-9} \times 9 \times 10^{9}}{0.031^{2}}~N~C^{-1}\\&or,& E = 2.81 \times 10^{4}~N~C^{-1}

3 0
3 years ago
Give reason as to why space is a quiet place?
Darina [25.2K]

Answer:A Quiet Place is a 2018 American horror film directed by and starring John Krasinski. Written by ... Four-year-old Beau is drawn to a battery-powered space shuttle toy, but Lee takes it away due ... Beau activates the toy when the family is walking home while crossing a bridge, giving away his location to a nearby creature that .

Explanation:

8 0
3 years ago
Other questions:
  • Rate my profile pic up to a 100
    8·1 answer
  • Material through which a wave passes
    11·1 answer
  • A mixed cost contains Select one:
    8·1 answer
  • How does energy move through an ecosystem?
    13·1 answer
  • A glass tube (open at both ends) of length L is positioned near an audio speaker of frequency f = 770 Hz. For what values of L w
    9·1 answer
  • What law of motion does this picture represent?​
    6·2 answers
  • A race car decelerating by 3 m /s to 10 m / s has an acceleration of 25
    14·1 answer
  • Can someone please help me match these up
    6·1 answer
  • A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of -2.0 m/s² and a final velocity of
    8·1 answer
  • True or False : If a car drives on a road for a nonzero amount of time, then its average velocity must be nonzero.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!