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Light passes through a diffraction grating with a slit spacing of 0.001 mm. A viewing screen is 100 cm behind the grating. If the light is blue, with a wavelength of 450 nm, at about what distance from the center of the interference pattern will the first-order maximum appear?
A. 5 cm   
B. 25 cm   
C. 50 cm   
D. 100 cm

Respuesta :

Answer:c

Explanation:

Given

Slit spacing [tex]d=0.001\ mm[/tex]

viewing screen is at a distance of [tex]D=100\ cm[/tex]

wavelength of light [tex]\lambda =450\ nm[/tex]

Condition for diffraction maxima is

[tex]d\sin \theta =m\lambda [/tex]

for first order maxima m=1

i.e. [tex]\theta =\sin ^{-1}(\frac{\lambda }{d})[/tex]

[tex]\theta =26.74^{\circ}[/tex]

Distance of first order maxima from center is

[tex]y=D\tan \theta [/tex]

[tex]y=0.1\tan (26.74)[/tex]

[tex]y=0.0503\ m[/tex]

[tex]y=50.38\ mm[/tex]