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  2. If one of the two slits of a Young's double slit experiment is painted over so that it transmits half the light intensity of the other, then: A. the fringe system would disappear B. the bright fringes would be brighter & dark fringes would be darker C.
# Engineering

If one of the two slits of a Young's double slit experiment is painted over so that it transmits half the light intensity of the other, then:

A. the fringe system would disappear

B. the bright fringes would be brighter & dark fringes would be darker

C. the dark fringes would be brighter and bright fringes would be darker

D. bright as well as dark fringes would be darker

Answers (1)
S Satyajeet Kumar

Case 1: When slit are of equal width, if $I_{0}$ is intensity of light then,
$\mathrm{I}_{\max }=\mathrm{I}_{\mathrm{o}}+\mathrm{I}_{\mathrm{o}}+2 \sqrt{\mathrm{I}_{\mathrm{o}} \mathrm{I}_{\mathrm{o}}}=4 \mathrm{I}_{\mathrm{o}}$ \\ $I_{\min }=I_{o}+I_{o}-2 \sqrt{I_{o} I_{o}}=0$ 
Case 2: When one of the slit is painted over, its intensity would reduce to half then,

$\mathrm{I}_{\mathrm{newmax}}=\mathrm{I}_{\mathrm{o}} / 2+\mathrm{I}_{\mathrm{o}}+2 \sqrt{\mathrm{I}_{\mathrm{o}} \mathrm{I}_{\mathrm{o}} / 2}=2.932 \mathrm{I}_{\mathrm{o}}$ 
$\mathrm{I}_{\mathrm{newmin}}=\mathrm{I}_{\mathrm{o}} / 2+\mathrm{I}_{\mathrm{o}}-2 \sqrt{\mathrm{I}_{\mathrm{o}} \mathrm{I}_{\mathrm{o}} / 2}=0.068 \mathrm{I}_{\mathrm{o}}$
Therefore, dark fringes get brighter and bright fringes get darker

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