In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is (1/8) th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

Question

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is (1/8) th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is : (A) 0.568 (B) 0.853 (C) 0.760 (D) 0.672

Tardigrade Admin · Accepted Answer

I=I0 cos2((Δφ/2)) (I/I0)=cos2((Δ φ /2)) (I/I0)=cos2(((2π/λ)×(λ/8)/2)) (I/I0)=cos2((π/8)) (I/I0)=0.853

Q. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}$ th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

$0.568$

$0.853$

$0.760$

$0.672$

$I = I_{0} co s^{2} (\frac{Δ ϕ}{2})$
$\frac{I}{I _{0}} = co s^{2} (\frac{Δ ϕ}{2})$
$\frac{I}{I _{0}} = co s^{2} (\frac{\frac{2 π}{λ} \times \frac{λ}{8}}{2})$
$\frac{I}{I _{0}} = co s^{2} (\frac{π}{8})$
$\frac{I}{I _{0}} = 0.853$

Q. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is 81​ th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

0.568

0.853

0.760

0.672