Question

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 Å is :- 

(1) 1178 × 10^–9 m

(2) 1178 × 10^–6 m

(3) 1178 × 10^–12 m

(4) 5890 × 10^–7 m

Answer 1

Correct option is (2) 1178 × 10^–6 m

= 589 × 10–6 m

Distance between first and third bright fringe is 2β = 2 × 589 × 10^–6 m

= 1178 × 10^–6 m

Answer 2

d = 0.5x10^-3m , D = 0.5m and wavelength = 589x10^-9m

distance of first bright from centre bright(CB) = Dλ/d

distance of 3rd bright from CB = 3Dλ/d

distance between 1st and 3rd bright fringe = 2Dλ/d = 2 x 0.5 x 589 x 10^-9/0.5 x 10^-3 

=1178 x 10^-6m