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 ${1.6}^{\circ} and {3.2}^{\circ}$

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

$d \sin θ_{m} = m λ$

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

$θ = \sin^{- 1} (\frac{m λ}{d})$

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 $d = \frac{1 cm}{500} = 2 \cdot 10^{- 5} m$ .

In our case, $\frac{λ}{d} = \frac{5.5 \cdot 10^{- 7}}{2 \cdot 10^{- 5}} = 0.0275 < < 1$ , which means we can apply the angle approximation to find the angle as $θ_{m} = \frac{m λ}{d}$ . We will then, for our angles, have $θ_{1} = 0.025 rad = 0.0275 \cdot \frac{360^{\circ}}{2 π} = {1.6}^{\circ}$

$θ_{1} = 0.025 rad = 0.0275 \cdot \frac{360^{\circ}}{2 π} = {1.6}^{\circ}$

$θ_{2} = 0.055 rad = 0.055 \cdot \frac{360^{\circ}}{2 π} = {3.2}^{\circ}$

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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)

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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

Quantum Physics

Measurements

Particle Model of Matter

Electricity

Further Mechanics and Thermal Physics

Fluids

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?