Chapter 33: Q. 14 (page 955)

A helium-neon laser $(λ = 633 nm)$ illuminates a diffraction grating. The distance between the two $m = 1$ bright fringes is $32 cm$ on a screen $2.0 m$ behind the grating. What is the spacing between slits of the grating $?$

Short Answer

Expert verified

Distance between slits of the grating is $7.9 μm$ .

Step by step solution

Formula for length between positions

The distance between the two $m = 1$ spots will be,

$ΔY = 2 {Ltanθ}_{1}$

$= 2 Ltan (\sin^{- 1} (\frac{λ}{d}))$

$\approx 2 Ltan (\frac{λ}{d})$

$d$ is grating space.

$λ$ is wavelength.

$θ_{1}$ is diffraction angle

Calculation for spacing of grating

Small angle,

x < < 1, x \approx \sin (x) \approx \tan (x)

Distance is,

$\tan (\frac{λ}{d}) = \frac{ΔY}{2 L}$

$\Rightarrow \frac{λ}{d} = \tan^{- 1} (\frac{ΔY}{2 L})$

So,

$d = \frac{λ}{\tan^{- 1} (\frac{ΔY}{2 L})}$

$= \frac{633 \cdot 10^{- 9}}{\tan^{- 1} (\begin{matrix} 0.32 \\ 2 \cdot 2 \end{matrix})}$

$= 7.9 μm$

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A helium-neon laser $(λ = 633 nm)$ illuminates a diffraction grating. The distance between the two $m = 1$ bright fringes is $32 cm$ on a screen $2.0 m$ behind the grating. What is the spacing between slits of the grating $?$

Short Answer

Step by step solution

Formula for length between positions

Calculation for spacing of grating

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A helium-neon laser (λ=633nm) illuminates a diffraction grating. The distance between the two m=1 bright fringes is 32cm on a screen 2.0m behind the grating. What is the spacing between slits of the grating?

Short Answer

Step by step solution

Formula for length between positions

Calculation for spacing of grating

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Further Mechanics and Thermal Physics

Magnetism and Electromagnetic Induction

Engineering Physics

Electricity and Magnetism

Dynamics

Study anywhere. Anytime. Across all devices.

A helium-neon laser $(λ = 633 nm)$ illuminates a diffraction grating. The distance between the two $m = 1$ bright fringes is $32 cm$ on a screen $2.0 m$ behind the grating. What is the spacing between slits of the grating $?$