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  • A wavefront presents one, two and three at points <img alt="\mathrm{A, B}

A wavefront presents one, two and three \mathrm{\mathrm{HPZ}} at points \mathrm{A, B} and \mathrm{C} respectively. If the ratio of consecutive amplitudes of HPZ is \mathrm{4: 3,} then the ratio of resultant intensities at these point will be

Option: 1

169 : 16 : 256


Option: 2

256 : 16 : 169


Option: 3

256 : 16 : 196


Option: 4

256 : 196 : 16


Answers (1)

best_answer

\mathrm{\begin{aligned} & I_A=R_1^2 \\\\ & I_B=\left(R_1-R_2\right)^2=R_1^2\left(1-\frac{R_2}{R_1}\right)^2=R_1^2\left(1-\frac{3}{4}\right)^2=\frac{R_1^2}{16} \\\\ & I_C=\left(R_1-R_2+R_3\right)^2=R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_1}\right)^2 \\\\ & =R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_2} \times \frac{R_2}{R_1}\right)^2=R_1^2\left(1-\frac{3}{4}+\frac{3}{4} \times \frac{3}{4}\right)^2=\left(\frac{13}{16}\right)^2 R_1^2=\frac{169}{256} R_1^2 \\\\ & \therefore I_A: I_B: I_C=R_1^2: \frac{R_1^2}{16}: \frac{169}{256} R_1^2=256: 16: 169 \end{aligned}}

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