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Q:- IN YOUNG DOUBLE SLIT EXPERIMENT SOURCE EMITS LIGHT OF WAVELENGTH 1mm AND DISTANCE BETWEEN SLIT AND SCREEN IS 100 cm THEN DISTANCE BETWEEN 3RD BLACK AND 5TH BRIGHT IS:-
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Answers
Wavelength of light (λ) = 1 mm .
Distance between the slit and the screen (D) is 100 cm .
Distance between the 3 rd dark fringe and the 5 th bright fringe = ?
If the fringe is dark , the distance of the fringe is :
( 2 n - 1 ) λ D / 2 d
If the fringe is dark , the distance of the fringe is :
n λ D / d
So the distance of 3 rd dark fringe is :
( 2×3 - 1 ) λ D / 2 d
⇒ ( 6 - 1 ) λ D / 2 d
⇒ 5 λ D / 2 d
The distance of the 5 th bright fringe is :
5 λ D / d
Distance between the 3 rd black and the 5 th bright is :
⇒ 5 λ D / d - ( 5 λ D / 2 d )
⇒ ( 10 λ D - 5 λ D ) / 2 d
⇒ 5 λ D / 2 d
Now putting the values of D , d and λ we get :
⇒ 5 × 1 mm × 100 cm / 2 d
1 mm = 1/10 cm ⇒ 1/1000 m
100 cm = 100/100 m ⇒ 1 m
⇒ [ 5 × ( 1/1000 ) × 1 m ] / 2 d
⇒ 5/ (2000 d ) m
⇒ 1 / ( 400 d ) m
⇒ 0.0025 d
The distance in metres between the 3 rd black and the 5 th bright is 0.0025 d .
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