White light containing wavelengths from 4.10E2 nm to7.50E2 nm falls on a grating with 7.8E3 lines/cm....

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White light containing wavelengths from 4.10E2 nm to7.50E2 nm falls on a grating with 7.8E3 lines/cm....

White light containing wavelengths from 4.10E2 nm to7.50E2 nm falls on a grating with 7.8E3 lines/cm. How wide is thefirst-order spectrum on a screen 2.70 m away?

Enter scientific notation as 1.23E4.

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Answer 1

Answer #1

d = 1/7.8E3cm = 1.28E-4 cm = 1.28E-6m , L =2.70 m,λ₁ = 4.10E2 nm, λ₂ =7.50E2 nm
first-orderbright line is at dsinθ =λ
sinθ₁ = λ₁/d= 0.320, y₁ = Ltanθ₁ = 0.91 m
sinθ₂ = λ₂/d = 0.586, y₂= Ltanθ₂ = 1.95 m
the reqiured width = 1.95 - 0.91 = 1.04 m

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Answer 2

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White light containing wavelengths from 4.10E2 nm to7.50E2 nm falls on a grating with 7.8E3 lines/cm....

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