Chapter 27: Q22PE (page 997)

Find the angle for the third-order maximum for $^{580 - nm}$ -wavelength yellow light falling on a diffraction grating having $^{1500}$ lines per centimeter.

Short Answer

Expert verified

The third-order maximum is obtained at an angle of $^{15 . 1^{0}}$ .

Step by step solution

Given data

Grating lines on the diffraction grating are 1500 liner per cm, which means that the distance between the two slits is $d = (\frac{1 cm}{1500}) (\frac{1 m}{100 cm}) = 6.67 \times 10^{- 6} m$

The wavelength of the yellow light is $λ = 580 nm (\frac{10^{- 9} m}{1 nm}) = 5.80 \times 10^{- 7} m$

The order of maximum is 3.

Evaluating the third-order maximum

For the given value of $^{θ}$ , and $^{λ}$ , the equation for the third-order maximum can be expressed as $d sinθ = 3 λ$ ,

The value of $^{θ}$ can be estimated from the above expression as,

$θ = \sin^{- 1} (\frac{λ}{d}) = \sin^{- 1} (\frac{3 \times 5.8 \times 10^{- 7} m}{6.67 \times 10^{- 6} m}) = \sin^{- 1} (0.261) = 15 . 1^{0}$

Therefore, the third-order maximum is, $^{15 . 1^{0}}$ .

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Find the angle for the third-order maximum for $^{580 - nm}$ -wavelength yellow light falling on a diffraction grating having $^{1500}$ lines per centimeter.

Short Answer

Step by step solution

Given data

Evaluating the third-order maximum

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Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a diffraction grating having 1500 lines per centimeter.

Short Answer

Step by step solution

Given data

Evaluating the third-order maximum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Measurements

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Space Physics

Electric Charge Field and Potential

Fields in Physics

Study anywhere. Anytime. Across all devices.

Find the angle for the third-order maximum for $^{580 - nm}$ -wavelength yellow light falling on a diffraction grating having $^{1500}$ lines per centimeter.