Chapter 33: Q. 39 (page 956)

A diffraction grating having $500 l i n e s / m m$ diffracts visible light at $30^{\circ}$ .What is the light's wavelength?

Short Answer

Expert verified

The wavelength of sunshine is $λ = 500 n m .$

Step by step solution

Step: 1 Finding the grating spacing:

The constant value of grating is $500 l i n e s / m m$ ,the spacing by

$d = \frac{1 mm}{500} d = \underset{}{2 \times 10^{- 6} m} .$

Step: 2 Equating the equation:

In equation of grating,the light diffraction light wavelength by

$d \sin (θ_{m}) = m λ \Rightarrow λ = \frac{d \sin (θ_{m})}{m} .$

Step: 3 Obtaining the wavelength value:

From expression of wavelength

$λ = \frac{2 \times 10^{- 6} \times \sin (30^{\circ})}{m} λ = \frac{1000 nm}{m} .$

As we're seeing, there should only be one value of $m$ that corresponds to a wavelength within the visible region and therfore the $m$ will be $2$ ,The wavelength are $500 n m$ .

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A diffraction grating having $500 l i n e s / m m$ diffracts visible light at $30^{\circ}$ .What is the light's wavelength?

Short Answer

Step by step solution

Step: 1 Finding the grating spacing:

Step: 2 Equating the equation:

Step: 3 Obtaining the wavelength value:

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A diffraction grating having 500lines/mmdiffracts visible light at 30∘.What is the light's wavelength?

Short Answer

Step by step solution

Step: 1 Finding the grating spacing:

Step: 2 Equating the equation:

Step: 3 Obtaining the wavelength value:

One App. One Place for Learning.

Most popular questions from this chapter

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A diffraction grating having $500 l i n e s / m m$ diffracts visible light at $30^{\circ}$ .What is the light's wavelength?