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ipn [44]
3 years ago
12

A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700 nm as part of a classroom demonstrat

ion. She shines a beam of white light through a diffraction grating that has 700 lines per mm, projecting a pattern on a screen 2.9 m behind the grating. How wide is the spectrum corresponding to m=1?
Physics
1 answer:
Zanzabum3 years ago
6 0

Answer:

Explanation:

Given

Slit\ width=d=\frac{10^{-3}}{700}=1.428\times 10^{-6} m

Distance of screen from light source D=2.9 m

\lambda _1=400 nm

\lambda _2=700 nm

we know in slit Experiment

d\sin \theta=n\lambda, where \theta=angle between the path and a line from the slits to the screen

1.428\times 10^{-6}\cdot \sin \theta =1\times 400\times 10^{-9}

\sin \theta =0.28011

\theta =16.26^{\circ}

and \tan \theta =\frac{y}{D}

where y is the position of First maxima corresponding \lambda _1

y_1=D\tan \theta

y_1=0.845 m

calculations for  \lambda _2

d\sin \theta=n\lambda _2

1.428\times 10^{-6}\cdot \sin \theta =1\times 700\times 10^{-9}

\sin \theta '=0.4901

\theta '=29.34^{\circ}

\tan \theta '=\frac{y'}{D}

for n=1

y_1'=D\tan \theta '

y_1'=2.9\times 0.5622=1.63 m

Spectrum Width =y_1'-y_1

=0.785 m

                   

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