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Lina20 [59]
3 years ago
5

A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700 nm as part of a classroom demonstrat

ion. She shines a beam of white light through a diffraction grating that has 600 lines per mm, projecting a pattern on a screen 2.9 m behind the grating.
Required:
How wide is the spectrum corresponding to m=1?
Physics
1 answer:
Likurg_2 [28]3 years ago
4 0

Answer:

  Dr = 263 10⁻⁶ m

Explanation:

The diffraction pattern for constructive interference is described by

        a sin θ = m λ

in this it indicates that the order of diffraction is m = 1

Let's use a direct proportion rule to find the separation of two slits. If there are 600 lines in 1 me, what is the distance between 2 slits

   a = 2 lines 1/600

   a = 2/600

    a = 3.33 10⁻³ mm = 3.33 10⁻⁴ cm

let's use trigonometry

      tan θ = y / L

as the measured angles are small

      tan θ = sin θ / cos θ sin θ

      sin θ = y / L

we substitute

     a  y/L = λ

     y = λ L / a

for λ = 400 10-9 m

      I = 400 10⁻⁹ 2.9 / 3.33 10⁻³

      i = 346.89 10⁻⁶ m

f

or λ = 700 nm

        y_f = 700 10⁻⁻⁹ 2.9 / 3.33 10⁻³

        y_f = 609.609 10⁻⁶ m

the separation of this spectrum

        Δr = v_f - i

        Dr = (609.609 - 346)  10 ⁻⁶

        Dr = 263 10⁻⁶ m

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klemol [59]

Answer:

Speed:

2.01x10^{8}m/s

Wavelength:

4.24x10^{-7}m

Frequency:

4.74x10^{14}Hz

Explanation:

The speed of the laser as it travels through polystyrene can be determine by means of the equation of the refraction index:

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Where c is the speed of light and v is the speed of the laser in the medium.

Therefore, v will be isolated from equation 1

v = \frac{c}{n}

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v = 2.01x10^{8}m/s

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Frenquency:

Since, wavelength is the only one who depends on the media. Therefore the frequency in both medium will be the same.  

To determine the frequency it can be used the following equation

c = \nu \cdot \lambda  (2)

Where c is the speed of light, \nu is the frequency and \lambda is the wavelength

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\nu = \frac{c}{\lambda}  (3)

Before using equation 3 it is necessary to express \lamba in units of meters.

\lambda = 632.8nm . \frac{1m}{1x10^{9}nm} ⇒ 6.328x10^{-7}m

\nu = \frac{3x10^{8}m/s}{6.328x10^{-7}m}

\nu = 4.74x10^{14}s^{-1}

\nu = 4.74x10^{14}Hz

Hence, the frequency of the laser has a value of 4.74x10^{14}Hz

Wavelength:

To determine the wavelength it can be used:

v = \nu \cdot \lambda

\lambda = \frac{v}{\nu}

Where v is the speed of the laser through the polystyrene.

\lambda = \frac{2.01x10^{8}m/s}{4.74x10^{14}s^{-1}}

\lambda = 4.24x10^{-7}m

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s344n2d4d5 [400]

Answer:

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