14. In the Young’s double-slit experiment, the intensity of light at a point on the screen where the path difference is λ is K, ( λ being the wave length of light used). The intensity at a point where the path difference is λ/4, will be :

14. In the Young’s double-slit experiment, the intensity of light at a point on the screen where the path difference is λ is K, ( λ being the wave length of light used). The intensity at a point where the path difference is λ/4, will be :

(a) K 

(b) K/4 

(c) K/2 

(d) 0

Answer :  (c) K/2

\( I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos \phi \)  

\( \text{phase diff.} = \dfrac{2\pi}{\lambda} \times \dfrac{\lambda}{4} \)  

\( = \dfrac{\pi}{2} \)  

\( I = I_1 + I_2 + (0) \)  

\( = 2I_1 \)  

\( = 2 \dfrac{K}{4} \)  

\( = \dfrac{K}{2} \)