Question

In YDSE, if the intensity of central maxima is I_O then the y-coordinate of point where the intensity is $\frac{I_{O}}{2}$, d = 0.1 mm,

D = 1m, l = 5000A°

• A. 1.5 mm
• B. 2 mm
• C. 1.75 mm
• D. 1.25 mm

Answer 1

Answer: (D)

1.25 mm

Answer 2

I = I ₀ cos² $\frac{\varphi}{2}$

$\frac{\mathbf{I}_{\mathbf{0}}}{\mathbf{2}}$ = I ₀ cos² $\frac{\varphi}{2}$

cos $\frac{\varphi}{2}$ = $\frac{1}{\sqrt{2}}$

f = 90⁰ ̃ f = $\frac{2\pi}{\lambda}$ Dx

$\frac{\pi}{2}$ = $\frac{2\pi}{\lambda}$ Dx

Dx = $\frac{\lambda}{4}$ ̃ $\frac{yd}{D}$ = $\frac{\lambda}{4}$

y = $\frac{\lambda D}{4d}$ = $\frac{5 \times 10^{- 7} \times 1}{4 \times 1 \times 10^{- 4}}$ = $\frac{5}{4}$ × 10^–3

y = 1.25 mm