Two coherent point sources S₁ and S₂ vibrating in phase emit light of wavelength . The separation between them is 2 as shown in figure. The first bright fringe is formed at P due to interference on a screen placed at a distance D from S₁(D>> ) , then O P is

Step-by-step solution

From the figure, aligned & (S₁ P )^2=D^2+x^2 & and & (S₂ P )^2=(D-2 )^2+x^2 & So, (S₁ P )^2- (S₂ P )^2=D^2+x^2 & - [D^2+4 ^2-4 D +x^2 ] & =4 D -4 ^2 & (S₁ P+S₂ P ) (S₁ P-S₂ P )=4 D -4 ^2 & [D>> ] & Since, [D>> ] & S₁ P=S₂ P & aligned and neglecting higher power of aligned & 2 S₁ P (S₁ P-S₂ P )=4 D & 2 (S₁ P )( )=4 D & or S₁ P=2 D & D^2+x^2 =2 D & x^2=3 D^2 & x= 3 D & aligned Alternative gathered 2 = = 1 2 =60^ , = x D 3 = x D x= 3 D gathered