Ratio of intensity of two waves is 25:36. If interference occurs, then ratio of maximum and minimum intensity should be .
A) 61 : 11
B) 5 : 6
C) 11 : 1
D) 121 : 1
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Ratio of intensity of two waves is 25:36. If interference occurs, then ratio of maximum and minimum intensity should be .
A) 61 : 11
B) 5 : 6
C) 11 : 1
D) 121 : 1
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Given :
Ratio of intensity of two waves = 25:36
To Find :
ratio of maximum and minimum intensity
Solution :
Let the intensities [tex]I_{1}[/tex] and [tex]I_{2}[/tex] be 25x and 36x respectively.
[tex]\frac{maximum intensity}{minimum intensity}[/tex] = [tex](\frac{\sqrt{I_{2} } + \sqrt{I_{1} } }{\sqrt{I_{2} } -\sqrt{I_{1} } })^{2}[/tex]
= [tex](\frac{\sqrt{36x } + \sqrt{25x_} }{\sqrt{36x} -\sqrt{25x } })^{2}[/tex]
= [tex](\frac{6\sqrt{x} + 5\sqrt{x} }{6\sqrt{x} - 5\sqrt{x} })^{2}[/tex]
= [tex]\frac{11\sqrt{x} }{\sqrt{x} }[/tex]
= [tex]\frac{11}{1}[/tex]
∴ The ratio of maximum and minimum intensity is 11:1.
The correct option is (c) 11:1
The ratio of intensities of two waves is 25 : 36.
if interference occurs , then the ratio of maximum and minimum intensity should be ..
A) 61 : 11
B) 5 : 6
C) 11 : 1
D) 121 : 1
when two waves of intensities I₁ and I₂ are interfere , then the intensity of resultant wave is given by,
[tex]\quad\bf I=\sqrt{I_1+I_2+2\sqrt{I_1I_2}cos\theta}[/tex]
for maximum intensity, θ = 0°
and maximum intensity,
[tex]I_{max}=\sqrt{(I_1+I_2+2\sqrt{I_1I_2})}=(\sqrt{I_1}+\sqrt{I_2})[/tex]
for minimum intensity, θ = 180°
and minimum intensity,
[tex]I_{min}=\sqrt{I_1+I_2-2\sqrt{I_1I_2}}=(\sqrt{I_1}-\sqrt{I_2})[/tex]
now the ratio of maximum intensity to minimum intensity is..
[tex]\frac{I_{max}}{I_{min}}=\left|\frac{(\sqrt{I_1}+\sqrt{I_2})}{(\sqrt{I_1}-\sqrt{I_2})}\right|[/tex]
= [tex]\left|\frac{\sqrt{\frac{I_1}{I_2}}+1}{\sqrt{\frac{I_1}{I_2}}-1}\right|[/tex]
here given, [tex]\frac{I_1}{I_2}=\frac{25}{36}[/tex]
= [tex]\left|\frac{\sqrt{\frac{25}{36}}+1}{\sqrt{\frac{25}{36}}-1}\right|[/tex]
= [tex]\left|\frac{5+6}{5-6}\right|[/tex]
= [tex]\frac{11}{1}[/tex]
Therefore the ratio of maximum intensity to minimum intensity is 11 : 1. hence option (C) is correct choice.