Chapter 33: Q. 49 (page 957)

$F I G U R E P 33.49$ shows the interference pattern on a screen $1.0 m$ behind an $800 l i n e / m m$ diffraction grating. What is the wavelength (in $m m$ ) of the light?

Short Answer

Expert verified

The wavelength's light is $λ = 500 n m .$

Step by step solution

Step: 1 Interference pattern:

When parallel plane waves of the same frequency meet at an angle, a simple sort of interference pattern results. Interference is fundamentally a process of energy redistribution. The energy wasted during destructive interference is recovered during positive interference.

Step: 2 Equating equation:

The angle of fringes as

$Y_{1} = L \tan (θ_{1}) θ_{1} = \tan^{- 1} (\frac{Y_{1}}{L})$

Equation of grating wavelength is

localid="1649148192850" $d \sin (θ_{1}) = λ = \frac{1 \times 10^{- 3}}{800} \sin (\tan^{- 1} (\frac{Y_{1}}{L}))$

Step: 3 Obtaining wavelength:

The wavelength to be

$λ = \frac{1 \times 10^{- 3}}{800} \sin (\tan^{- 1} (\frac{0.436}{1})) λ = 1.25 \times 10^{- 6} \sin ({23.56}^{\circ}) λ = 5.00 \times 10^{- 7} m λ = 500 nm .$

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$F I G U R E P 33.49$ shows the interference pattern on a screen $1.0 m$ behind an $800 l i n e / m m$ diffraction grating. What is the wavelength (in $m m$ ) of the light?

Short Answer

Step by step solution

Step: 1 Interference pattern:

Step: 2 Equating equation:

Step: 3 Obtaining wavelength:

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FIGUREP33.49shows the interference pattern on a screen 1.0mbehind an 800line/mmdiffraction grating. What is the wavelength (in mm) of the light?

Short Answer

Step by step solution

Step: 1 Interference pattern:

Step: 2 Equating equation:

Step: 3 Obtaining wavelength:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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$F I G U R E P 33.49$ shows the interference pattern on a screen $1.0 m$ behind an $800 l i n e / m m$ diffraction grating. What is the wavelength (in $m m$ ) of the light?