Q155 / 200 · MHT CET - Medical 2026 (21 April Shift 1) · Physics
The equation of two interfering light waves are
$y_1 = b \cos \omega t$ and $y_2 = b \sin(\omega t + \Phi)$.
If the light waves interfere destructively, then the possible value of $\Phi$ are
$y_1 = b \cos \omega t$ and $y_2 = b \sin(\omega t + \Phi)$.
If the light waves interfere destructively, then the possible value of $\Phi$ are
- A$\dfrac{3\pi}{2}, \dfrac{5\pi}{2}, \dfrac{13\pi}{2}, \ldots\ldots$
- B$\dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{13\pi}{2}, \ldots$
- Correct answerC$\dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{11\pi}{2}, \ldots\ldots$
- D$\dfrac{3\pi}{2}, \dfrac{9\pi}{2}, \dfrac{11\pi}{2}, \ldots\ldots$
Solution
The given equations of the light waves are:
$y_1 = b \cos \omega t = b \sin\left(\omega t + \dfrac{\pi}{2}\right)$
$y_2 = b \sin(\omega t + \Phi)$
The phase difference between the two waves is:
$\Delta \phi = (\omega t + \Phi) - \left(\omega t + \dfrac{\pi}{2}\right) = \Phi - \dfrac{\pi}{2}$
For destructive interference, the phase difference must be an odd multiple of $\pi$:
$\Delta \phi = (2n - 1)\pi$
$\Phi - \dfrac{\pi}{2} = (2n - 1)\pi$
$\Phi = (2n - 1)\pi + \dfrac{\pi}{2} = \dfrac{(4n - 1)\pi}{2}$
Substituting $n = 1, 2, 3, \ldots$, we get the possible values of $\Phi$:
$\Phi = \dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{11\pi}{2}, \ldots$
Answer: $\dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{11\pi}{2}, \ldots\ldots$
$y_1 = b \cos \omega t = b \sin\left(\omega t + \dfrac{\pi}{2}\right)$
$y_2 = b \sin(\omega t + \Phi)$
The phase difference between the two waves is:
$\Delta \phi = (\omega t + \Phi) - \left(\omega t + \dfrac{\pi}{2}\right) = \Phi - \dfrac{\pi}{2}$
For destructive interference, the phase difference must be an odd multiple of $\pi$:
$\Delta \phi = (2n - 1)\pi$
$\Phi - \dfrac{\pi}{2} = (2n - 1)\pi$
$\Phi = (2n - 1)\pi + \dfrac{\pi}{2} = \dfrac{(4n - 1)\pi}{2}$
Substituting $n = 1, 2, 3, \ldots$, we get the possible values of $\Phi$:
$\Phi = \dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{11\pi}{2}, \ldots$
Answer: $\dfrac{3\pi}{2}, \dfrac{7\pi}{2}, \dfrac{11\pi}{2}, \ldots\ldots$
Hence, the correct answer is option: 'C'.