Respuesta :

sharmaenderp
To find the wavelength of the light that illuminates the diffraction grating, we must recall that wavelength, λ, can be computed through the diffraction formula below.

[tex] d \sin{\theta} = \lambda [/tex]

where d is the width of the slits of the diffraction grating and θ is the diffraction angle. 

For this case, we have d = 1/750 mm. Thus, we have

[tex] (\frac{1}{750})\sin(34) = \lambda [/tex]
[tex] \lambda = 0.000746 mm [/tex]

Since wavelengths are usually expressed in nanometers, we have λ = 746 x 10⁻⁹ m or 746 nm.

Answer: 746 nm.
johanrusli

The wavelength of the light is about 7.46 × 10⁻⁷ m

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Further explanation

Let's recall diffraction grating formula as follows:

[tex]\large {\boxed { d \sin \theta = n \lambda } }[/tex]

where:

d = distance between the slits ( m )

θ = diffraction angle ( radian )

n = order number

λ = wavelength of light ( m )

Let's now tackle the problem!

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Complete Question:

A diffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0°. What is the wavelength of the light?

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Given:

Number of slits = N = 750 slits/mm

Difraction angle = θ = 34.0°

Order Number = n = 1

Asked:

Wavelength = λ = ?

Solution:

[tex]d \sin \theta = n \lambda[/tex]

[tex]\frac{1}{N} \sin \theta = n \lambda[/tex]

[tex]\lambda = \sin \theta \div ( Nn )[/tex]

[tex]\lambda = \sin 34.0^o \div ( 750 \times 1 )[/tex]

[tex]\lambda = 7.46 \times 10^{-4} \texttt{ mm}[/tex]

[tex]\lambda = 7.46 \times 10^{-7} \texttt{ m}[/tex]

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Learn more

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Answer details

Grade: High School

Subject: Physics

Chapter: Light

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