# In Young’s double slit experiment the intensity of light at a point on the screen where the path difference is λ is K…..

Q. In Young’s double slit experiment the intensity of light at a point on the screen where the path difference is λ  is K. The intensity of light at a point where the path difference is  λ /3 [ λ is the wavelength of light used] is

(a) K/4

(b) K/3

(c) K/2

(d) K

Ans: (a)
Sol: $\displaystyle I_R = I_1 + I_2 + 2 \sqrt{I_1 \times I_2 } cos\phi$

$\displaystyle I_R = I + I + 2 \sqrt{I \times I } cos\phi$

$\displaystyle I_R = 2I(1 + cos\phi)$

$\displaystyle I_R = 2I(2 cos^2 \frac{\phi}{2})$

$\displaystyle I_R = 4 I cos^2 \frac{\phi}{2}$

According to question , $\displaystyle K = 4 I cos^2 \pi$ (As path diff. is λ hence phase diff. is 2π)

$\displaystyle K = 4 I$ ….(i)

In second case ,

$\displaystyle I_R’ = 4 I cos^2 \frac{\phi’}{2}$

$\displaystyle I_R’ = 4 I cos^2 \frac{\pi}{3}$ (As path diff. is λ/3 hence phase diff. is 2π/3)

$\displaystyle I_R’ = 4 I \times \frac{1}{4}= I$

$\displaystyle I_R’ = I = \frac{K}{4}$