The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9: 1. The intensities of the used light sources are in ratio

Question

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9: 1. The intensities of the used light sources are in ratio (A) 3: 1 (B) 4: 1 (C) 9: 1 (D) 10: 1

Tardigrade Admin · Accepted Answer

(Imax/Imin)=((a+b)2/(a-b)2) (9/1)=((a+b)2/(a-b)2) or (3/1)=(a+b/a-b) or 3a-3b = a+b or 2a = 4b or a = 2b ∴ (I1/I2)=(a2/b2)=(4/1)

Q. The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9 : 1. The intensities of the used light sources are in ratio

3 : 1

4 : 1

9 : 1

10 : 1

$\frac{I _{ma x}}{I _{min}} = \frac{( a + b ) ^{2}}{( a - b ) ^{2}}$
$\frac{9}{1} = \frac{( a + b ) ^{2}}{( a - b ) ^{2}}$
or $\frac{3}{1} = \frac{a + b}{a - b}$ or 3a-3b = a+b
or 2a = 4b or a = 2b
$∴ \frac{I _{1}}{I _{2}} = \frac{a ^{2}}{b ^{2}} = \frac{4}{1}$

Q. The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9 : 1. The intensities of the used light sources are in ratio

3 : 1

4 : 1

9 : 1

10 : 1

Imin​Imax​​=(a−b)2(a+b)2​ 19​=(a−b)2(a+b)2​ or 13​=a−ba+b​ or 3a-3b = a+b or 2a = 4b or a = 2b ∴I2​I1​​=b2a2​=14​

$\frac{I _{ma x}}{I _{min}} = \frac{( a + b ) ^{2}}{( a - b ) ^{2}}$
$\frac{9}{1} = \frac{( a + b ) ^{2}}{( a - b ) ^{2}}$
or $\frac{3}{1} = \frac{a + b}{a - b}$ or 3a-3b = a+b
or 2a = 4b or a = 2b
$∴ \frac{I _{1}}{I _{2}} = \frac{a ^{2}}{b ^{2}} = \frac{4}{1}$