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Two waves coming from two coherent sources of different intensities interfere. The ratio of the maximum intensity to the minimum intensity is 25. The intensities of the two sources are in the ratio

Asked in GUJCET 2007 · Intensity and coherent sources

• (1) 25:1
• (2) 25:16
• (3) 9:4
• (4) 5:1

Step-by-step solution

Why the other options are wrong

• (1) Takes the source ratio to be (Iₘₐₓ)/(Iₘᵢₙ) itself. The two are different: (I₁)/(I₂)=(25)/1 would give (Iₘₐₓ)/(Iₘᵢₙ)=((5+1)/(5-1))²=2.25, not 25.
• (2) No single slip turns 25 into 25:16. Sanity check: for I₁:I₂=25:16 the amplitudes are in the ratio 5:4, so (Iₘₐₓ)/(Iₘᵢₙ)=((5+4)/(5-4))²=81.
• (4) 5:1 is √25, which is the amplitude ratio (a₁+a₂)/(a₁-a₂) of the resultant, not the ratio of the source intensities. Solving (a₁+a₂)/(a₁-a₂)=5 gives a₁:a₂=3:2.

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