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

256 : 16 : 169

$I_{A}=R_1^2$

$I_{B}=\left(R_1-R_2\right)^2=R_1^2\left(1-\frac{R_2}{R_1}\right)^2=R_1^2\left(1-\frac{3}{4}\right)^2=\frac{R_1^2}{16}$

$I_{C}=\left(R_1-R_2+R_3\right)^2=R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_1}\right)^2$

$=R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_2} \times \frac{R_{R}}{R_1}\right)^2=R_1^2\left(1-\frac{3}{4}+\frac{3}{4} \times \frac{3}{4}\right)^2=\left(\frac{13}{16}\right)^2 R_1^2=\frac{169}{256} R_1^2$

∴ $I_{A}: I_{B}: I_{C}=R_1^2: \frac{R_1^2}{16}: \frac{169}{256} R_1^2=256: 16: 169$