Q.9 A 4.0-cm-wide diffraction gratin... [FREE SOLUTION]

Chapter 33: Q.9 (page 955)

A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength $550 nm$ . What are the angles (in degrees) of the first two diffraction orders?

Short Answer

Expert verified

The angle in degree of the first two diffraction order is ${1.6}^{鈭�} and {3.2}^{鈭�}$

Step by step solution

Find angle(part a)

We know that the formula for a diffraction grating connecting the m-t h diffraction angle, the order m of the diffraction, the wavelength, and the space between two consecutive gratings is

$d \sin 鈦� 胃_{m} = m 位$

As a result, the angle at which m-t h order diffraction is observed is

$胃 = \sin^{鈭� 1} 鈦� (\frac{m 位}{d})$

Find angle(part b)

Knowing that there are 2000 gratings in $4 cm$ , the grating constant will be $500 l / cm$ . This means that the separation d is $d = \frac{1 cm}{500} = 2 路 10^{- 5} m$ .

In our case, $\frac{位}{d} = \frac{5.5 路 10^{- 7}}{2 路 10^{- 5}} = 0.0275 < < 1$ , which means we can apply the angle approximation to find the angle as $胃_{m} = \frac{m 位}{d}$ . We will then, for our angles, have $胃_{1} = 0.025 rad = 0.0275 鈰� \frac{360^{鈭�}}{2 蟺} = {1.6}^{鈭�}$

$胃_{1} = 0.025 rad = 0.0275 鈰� \frac{360^{鈭�}}{2 蟺} = {1.6}^{鈭�}$

$胃_{2} = 0.055 rad = 0.055 鈰� \frac{360^{鈭�}}{2 蟺} = {3.2}^{鈭�}$

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91影视

A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength $550 nm$ . What are the angles (in degrees) of the first two diffraction orders?

Short Answer

Step by step solution

Find angle(part a)

Find angle(part b)

One App. One Place for Learning.

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91影视

A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength 550nm. What are the angles (in degrees) of the first two diffraction orders?

Short Answer

Step by step solution

Find angle(part a)

Find angle(part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Energy Physics

Quantum Physics

Solid State Physics

Famous Physicists

Dynamics

Study anywhere. Anytime. Across all devices.

A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength $550 nm$ . What are the angles (in degrees) of the first two diffraction orders?