In YDSE , intensity at central maxima is I0 . The ratio (I/I0) , at path difference (λ /8) on the screen from central maxima, is closed to

Question

In YDSE , intensity at central maxima is I0 . The ratio (I/I0) , at path difference (λ /8) on the screen from central maxima, is closed to (A) 0.74 (B) 0.8  (C) 0.9  (D) 0.85

Tardigrade Admin · Accepted Answer

Δ φ=(2 π /λ )× (λ /8)=(π /4) I=I0cos2 (π /8) =I0((1 + cos π / 4/2)) =I0((1 + (1/√2)/2))=0.85 I0

Q. In $Y D SE$ , intensity at central maxima is $I_{0}$ . The ratio $\frac{I}{I _{0}}$ , at path difference $\frac{λ}{8}$ on the screen from central maxima, is closed to

$0.74$

$0.8$

$0.9$

$0.85$

$Δ ϕ = \frac{2 π}{λ} \times \frac{λ}{8} = \frac{π}{4}$
$I = I_{0} co s^{2} \frac{π}{8}$
$= I_{0} (\frac{1 + cos π /4}{2})$
$= I_{0} (\frac{1 + \frac{1}{2}}{2}) = 0.85 I_{0}$

Q. In YDSE , intensity at central maxima is I0​ . The ratio I0​I​ , at path difference 8λ​ on the screen from central maxima, is closed to

0.74

0.8

0.9

0.85