A wavefront presents one, two and three HPZ at points A, B and C … - Vidyadip

MCQ

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

A
$169: 16: 256$
✓
$256: 16: 169$
C
$256: 16: 196$
D
$256: 196: 16$

✓

Answer

Correct option: B.

$256: 16: 169$

$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_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 $
$\therefore I_A: I_B: I_C=R_1^2: \frac{R_1^2}{16}: \frac{169}{256} R_1^2=256: 16: 169$

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