Chapter 33: Q. 12 (page 955)

A diffraction grating is illuminated simultaneously with red light of wavelength $660 nm$ and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength $?$

Short Answer

Expert verified

The unknown wavelength is $369 nm$ .

Step by step solution

Formula for diffraction angle

We know that for an incident light of wavelength $λ$ , the $m$ -th order diffraction angle is,

$θ_{m, λ} = \sin^{- 1} (\frac{mλ}{d})$

θ

is diffraction angle

$λ$ is wavelength

$d$ is diffraction spacing

Calculation for unknown wavelength

We might equate the overlapping situation with

$Y_{3, red} = Y_{5, ukn.} \Rightarrow {Ltanθ}_{3, red}$

${Ltanθ}_{5, ukn.} \Rightarrow θ_{3, red}$

${Ltanθ}_{5, ukn.} \Rightarrow θ_{3, red} = θ_{5, unk}$

Y_{3, red} = Y_{5, ukn.} \Rightarrow {Ltanθ}_{3, red} = {Ltanθ}_{5, ukn.} \Rightarrow θ_{3, red} = θ_{5, unk}

So,

$\frac{3 \times λ_{red}}{d} = \frac{5 \times λ}{d}$

$λ = \frac{3 \times λ_{red}}{5} = 0.6 \times 660$

$= 396 nm$

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A diffraction grating is illuminated simultaneously with red light of wavelength $660 nm$ and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength $?$

Short Answer

Step by step solution

Formula for diffraction angle

Calculation for unknown wavelength

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A diffraction grating is illuminated simultaneously with red light of wavelength660nmand light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength?

Short Answer

Step by step solution

Formula for diffraction angle

Calculation for unknown wavelength

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Measurements

Medical Physics

Torque and Rotational Motion

Rotational Dynamics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

A diffraction grating is illuminated simultaneously with red light of wavelength $660 nm$ and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength $?$