Physics, 10.10.2019 20:30, nubsies31

Adiffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0 ? .

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To find the wavelength of the light that illuminates the diffraction grating, we must recall that wavelength, λ, can be computed through the diffraction formula below.

$d \sin{\theta} = \lambda$

where d is the width of the slits of the diffraction grating and θ is the diffraction angle.

For this case, we have d = 1/750 mm. Thus, we have

$(\frac{1}{750})\sin(34) = \lambda$
$\lambda = 0.000746 mm$

Since wavelengths are usually expressed in nanometers, we have λ = 746 x 10⁻⁹ m or 746 nm.

746 nm.

answered: micahwilkerson9495

The wavelength of the light is about 7.46 × 10⁻⁷ m

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Further explanation

Let's recall diffraction grating formula as follows:

$\large {\boxed { d \sin \theta = n \lambda } }$

where:

d = distance between the slits ( m )

θ = diffraction angle ( radian )

n = order number

λ = wavelength of light ( m )

Let's now tackle the problem!

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Complete Question:

A diffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0°. What is the wavelength of the light?

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Given:

Number of slits = N = 750 slits/mm

Difraction angle = θ = 34.0°

Order Number = n = 1

Asked:

Wavelength = λ = ?

Solution:

$d \sin \theta = n \lambda$

$\frac{1}{N} \sin \theta = n \lambda$

$\lambda = \sin \theta \div ( Nn )$

$\lambda = \sin 34.0^o \div ( 750 \times 1 )$

$\lambda = 7.46 \times 10^{-4} \texttt{ mm}$

$\lambda = 7.46 \times 10^{-7} \texttt{ m}$

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Learn moreSharpness and Resolution of Line Spectrum : Balmer Series : The Wavelength of Visible Light Waves :

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Answer details

Grade: High School

Subject: Physics

Chapter: Light

$Adiffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffrac$

answered: Guest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

answered: Guest

The sample with the lowest specific heat capacity will have the greatest temperature increase. in this case, it would be platinum.

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Adiffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffrac...