The intensity ratio in the interference pattern is 1:9 what is the amplitude ratio and the ratio of the widths of the two slits
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let the amplitude of two waves interfering be A1 and A2. Intensities be I1 and I2 of the two waves.
amplitude of the light in the bright region = A1+A2
amplitude of the light wave in dark/low intensity region = A1 - A2
ratio of intensities = (A1-A2)² /(A1 + A2)² = 1 : 9 given
=> (A1-A2)/(A1+A2 ) = 1/3
=> A1 /A2 = 2 : 1
Ratio of amplitudes = 1 : 2 or 2 : 1
Ratio of intensities of the interfering waves : = A1² / A2² = 4 : 1
The two intensity of the interfering waves that pass through a slit is dependent on the amount of light passing through the slit. So intensity is proportional to the slit width. (Slit breadth is same for both slits.)
Hence ratio of the widths of slits = 4 : 1
amplitude of the light in the bright region = A1+A2
amplitude of the light wave in dark/low intensity region = A1 - A2
ratio of intensities = (A1-A2)² /(A1 + A2)² = 1 : 9 given
=> (A1-A2)/(A1+A2 ) = 1/3
=> A1 /A2 = 2 : 1
Ratio of amplitudes = 1 : 2 or 2 : 1
Ratio of intensities of the interfering waves : = A1² / A2² = 4 : 1
The two intensity of the interfering waves that pass through a slit is dependent on the amount of light passing through the slit. So intensity is proportional to the slit width. (Slit breadth is same for both slits.)
Hence ratio of the widths of slits = 4 : 1
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