Chapter 36: Q14Q (page 1108)

For a certain diffraction grating, the ratio $λ / a$ of wavelength to ruling spacing is $1 / 3.5$ . Without written calculation or the use of a calculator, determine which of the orders beyond the zeroth order appear in the diffraction pattern.

Short Answer

Expert verified

The orders are 1,2 and 3 appear in the diffraction pattern.

Step by step solution

Given data

The ratio of the wavelength to slit width, $λ / a = 1 / 3.5$

Determine the formula orders that appear in the diffraction pattern.

The expression for the minima in the diffraction pattern is given as follows.

$asinθ = mλ$

Here,

a

is the slit width,

λ

is the wavelength,

m

is the number of the fringes in the envelop and

θ

is the angle of diffraction.

Calculate the orders that appear in the diffraction pattern.

The maximum angle for which diffraction can occur is .

Recall the equation (i),

$a \sin θ = m λ \frac{λ}{a} = \frac{\sin θ}{m_{\max}}$

Substitute $1 / 3.5$ for $λ / a$ and $90 °$ for $θ$ into above equation.

$\frac{1}{3.5} = \frac{\sin 90 °}{m_{\max}} \frac{1}{3.5} = \frac{1}{m_{\max}} m_{\max} = 3.5$

Since the maximum value of the number of the fringes in the envelop is 3.5, therefore, the orders are 1, 2 and 3 appear in the diffraction pattern.

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For a certain diffraction grating, the ratio $λ / a$ of wavelength to ruling spacing is $1 / 3.5$ . Without written calculation or the use of a calculator, determine which of the orders beyond the zeroth order appear in the diffraction pattern.

Short Answer

Step by step solution

Given data

Determine the formula orders that appear in the diffraction pattern.

Calculate the orders that appear in the diffraction pattern.

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For a certain diffraction grating, the ratio λ/aof wavelength to ruling spacing is1/3.5. Without written calculation or the use of a calculator, determine which of the orders beyond the zeroth order appear in the diffraction pattern.

Short Answer

Step by step solution

Given data

Determine the formula orders that appear in the diffraction pattern.

Calculate the orders that appear in the diffraction pattern.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Engineering Physics

Nuclear Physics

Electricity and Magnetism

Famous Physicists

Dynamics

Study anywhere. Anytime. Across all devices.

For a certain diffraction grating, the ratio $λ / a$ of wavelength to ruling spacing is $1 / 3.5$ . Without written calculation or the use of a calculator, determine which of the orders beyond the zeroth order appear in the diffraction pattern.