Chapter 33: Q. 45 (page 957)

White light $(400 - 700 n m)$ incident on a $600 l i n e / m m$ diffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen $2.0 m$ behind the grating?

Short Answer

Expert verified

On a screen behind the grating, the breadth of the rainbow is $0.43 m .$

Step by step solution

Step: 1 Diffraction grating:

A optical device is an device that splits multicoloured light into its beam is split (disperses colors). The polychromatic light received on the grating is scattered, ends up in each wavelength becoming reflected at a replacement angle from the grating.

Step: 2 Finding position:

The fringe position by

$Y_{m} = L \tan (θ_{m})$

The angle by

localid="1649097338452" $d \sin (θ_{m}) = m λ \Rightarrow θ_{m} = \sin^{- 1} (\frac{m λ}{d}) Y_{m} = L \tan (\sin^{- 1} (\frac{m λ}{d}))$

Step: 3 Finding the width:

Two variable wavelength by

$Δ Y_{m} = L [\tan (\sin^{- 1} (\frac{m λ_{2}}{d})) - \tan (\sin^{- 1} (\frac{m λ_{1}}{d}))]$

where,

localid="1649148081063" $d = 1 mm / 600 d = 5 / 3 \times 10^{- 6} m .$

The rainbow width by

localid="1649156772212" $Δ Y_{1} = 2 \times [\tan (\sin^{- 1} (\frac{7 \times 10^{- 7}}{5 / 3 \times 10^{- 6}})) - \tan (\sin^{- 1} (\frac{4 \times 10^{- 7}}{5 / 3 \times 10^{- 6}}))] Δ Y_{1} = 0.43 m .$

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White light $(400 - 700 n m)$ incident on a $600 l i n e / m m$ diffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen $2.0 m$ behind the grating?

Short Answer

Step by step solution

Step: 1 Diffraction grating:

Step: 2 Finding position:

Step: 3 Finding the width:

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White light400-700nmincident on a 600line/mmdiffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen 2.0mbehind the grating?

Short Answer

Step by step solution

Step: 1 Diffraction grating:

Step: 2 Finding position:

Step: 3 Finding the width:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Electricity

Thermodynamics

Further Mechanics and Thermal Physics

Scientific Method Physics

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.

White light $(400 - 700 n m)$ incident on a $600 l i n e / m m$ diffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen $2.0 m$ behind the grating?