In Young's double slit experiment, the fringe width is 2 ~mm . The separation between the 13^ th bright fringe and the 4^ th dark fringe from the centre of the screen on same side will be

Step-by-step solution

Given: Fringe width W =2 ~mm The distance of the n ^ th bright fringe from centre of the screen y _ n = n D d ... (i) The distance of the n ^ th dark fringe from centre of the screen y_n^ =(2 n-1) D 2 d ... (ii) Substituting, n =13 in (i) and n =4 in (ii) we get y ₁₃= 13 D d and y ₄^ = 7 2 D d The separation between the 13^ th bright fringe and the 7^ th dark fringe is aligned & y ₁₃- y ₄^ & = 13 D d - 7 2 D d & = (13- 7 2 ) D d & = 19 2 D d = 19 2 ~W & & but W =2 ~mm & y ₁₃- y ₄^ = 19 2 2=19 ~mm aligned