Question

# The green light of wavelengths $$100$$A from a narrow slit is incident on a double slit. If the overall separation of $$10$$ fringes on a screen $$200$$cm away is $$2$$cm, find the slit separation?

A
105 m
B
107 m
C
106 m
D
108 m

Solution

## The correct option is C $$10^{-5}$$ mThe wavelength of the green light$$\lambda =100A^{ 0 }$$ $$=100\times 10^{ - }10m$$ $$=10^{ - }8m$$The distance between screen and slit is given as $$D = 200 cm=2m$$.The separation between 10 fringes is given as $$2$$ cm. Hence, the fringe width is calculated as$$\beta =\frac { 2 }{ 10 } cm$$ $$=0.2cm$$ $$=0.002m$$We are asked to calculate the slit width$$[ d ]$$ The fringe width is calculated as follows $$\beta =\frac { \lambda D }{ d }$$ $$⇒d=\frac { \lambda D }{ \beta }$$ $$=\frac { 10^{ - }8\times 2 }{ 0.002 } m$$ $$=10^{ -5 }m$$ PhysicsNCERTStandard XII

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