In Young's double slit experiment, if the widths of the slits are in the ratio 4: 9, the ratio of the intensity at maxima to the intensity at minima will be

Question

In Young's double slit experiment, if the widths of the slits are in the ratio 4: 9, the ratio of the intensity at maxima to the intensity at minima will be (A) 169: 25 (B) 81: 16 (C) 25: 1 (D) 9: 4

Tardigrade Admin · Accepted Answer

Slit width ratio =4: 9; hence I1: I2=4: 9 ∴ (a12/a22)=(4/9) ⇒ (a1/a2)=(2/3) ∴ (I max /I min )=((a1+a2)2/(a1-a2)2)=(25/1)

Q. In Young's double slit experiment, if the widths of the slits are in the ratio $4 : 9$ , the ratio of the intensity at maxima to the intensity at minima will be

169 : 25

81 : 16

25 : 1

9 : 4

Slit width ratio $= 4 : 9$ ;
hence $I_{1} : I_{2} = 4 : 9$
$∴ \frac{a _{1}^{2}}{a _{2}^{2}} = \frac{4}{9}$
$\Rightarrow \frac{a _{1}}{a _{2}} = \frac{2}{3}$
$∴ \frac{I _{m a x}}{I _{m i n}} = \frac{( a _{1} + a _{2} ) ^{2}}{( a _{1} - a _{2} ) ^{2}} = \frac{25}{1}$

Q. In Young's double slit experiment, if the widths of the slits are in the ratio 4:9, the ratio of the intensity at maxima to the intensity at minima will be