Respuesta :
Answer:
Explanation:
Given
[tex]Slit\ width=d=\frac{10^{-3}}{700}=1.428\times 10^{-6} m[/tex]
Distance of screen from light source [tex]D=2.9 m[/tex]
[tex]\lambda _1=400 nm[/tex]
[tex]\lambda _2=700 nm[/tex]
we know in slit Experiment
[tex]d\sin \theta=n\lambda [/tex], where [tex]\theta [/tex]=angle between the path and a line from the slits to the screen
[tex]1.428\times 10^{-6}\cdot \sin \theta =1\times 400\times 10^{-9}[/tex]
[tex]\sin \theta =0.28011[/tex]
[tex]\theta =16.26^{\circ}[/tex]
and [tex]\tan \theta =\frac{y}{D}[/tex]
where y is the position of First maxima corresponding [tex]\lambda _1[/tex]
[tex]y_1=D\tan \theta [/tex]
[tex]y_1=0.845 m[/tex]
calculations for [tex]\lambda _2[/tex]
[tex]d\sin \theta=n\lambda _2[/tex]
[tex]1.428\times 10^{-6}\cdot \sin \theta =1\times 700\times 10^{-9}[/tex]
[tex]\sin \theta '=0.4901[/tex]
[tex]\theta '=29.34^{\circ}[/tex]
[tex]\tan \theta '=\frac{y'}{D}[/tex]
for n=1
[tex]y_1'=D\tan \theta '[/tex]
[tex]y_1'=2.9\times 0.5622=1.63 m[/tex]
Spectrum Width [tex]=y_1'-y_1[/tex]
[tex]=0.785 m[/tex]
0.785m is the width of the spectrum which corresponds to m=1.
What is width?
This is defined as the measurement of a body from side to side and usually has the shortest dimension.
Slit width = d = 10⁻³ / 700 = 1.428 ˣ 10⁻⁶m
In slit experiment dsinθ = nλ
1.428 ˣ 10⁻⁶m ˣ sinθ = 1 ˣ 400 ˣ 10⁻⁹
sinθ = 0.28011
θ = 16.26°
tanθ = y/D
y1 = Dtanθ
y1 = 0.845m
dsinθ2 = nλ2
1.428 ˣ 10⁻⁶m ˣ sinθ = 1 ˣ 700 ˣ 10⁻⁹
sinθ2 = 0.4901
θ2 = 29.34°
tanθ2 = y2/D
y2 = Dtanθ2
= 2.9 × 0.5622 = 1.63m
Spectrum Width = y2 - y
= 1.63m - 0.845m
= 0.785m.
Read more about Spectrum width here https://brainly.com/question/6441762
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