PYQ Wovrix CBSE 12
Physics Wave Optics 5 Marks
Appeared in: 2022 (3 sets)
The principle of superposition is used to understand the phenomenon of interference of light waves. The principle states that at a particular point, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each wave. Light waves from two coherent sources produce interference pattern. Thomas Young devised a way to obtain two coherent sources using two identical pinholes ($S_1$ and $S_2$) illuminated by a single monochromatic pinhole source S. Using these sources in his experiment known as Young’s double slit experiment, Young studied the interference pattern. The pattern consists of alternate bright and dark fringes. The distance between two successive bright or dark fringes depends on the distance between $S_1$ and $S_2$, the distance of the screen from the plane of $S_1S_2$ and the wavelength of light used. I. Consider the following waves: (i) $y_1 = a \sin \omega t$ (ii) $y_2 = a \sin 2\omega t$ (iii) $y_3 = a \sin $2\omega t + \phi$$ (iv) $y_4 = a \sin $4\omega t + \frac{\pi}{2}$$ Which pair of the waves coming from two sources $S_1$ and $S_2$ will produce interference? (A) (i) and (ii) (B) (ii) and (iii) (C) (iii) and (iv) (D) (iv) and (i)
✓ Verified CBSE Marking Scheme Official Evaluation Steps & EL10 Insight

Question Analysis: To produce a stable interference pattern, the two light waves must be coherent. Coherent sources must have the same frequency (or wavelength) and a constant phase difference over time.

Step 1 (Governing Law & Condition for Interference): [1 Mark]

For two waves to produce a sustained interference pattern, they must be coherent. The fundamental condition for coherence is that the waves must have the same angular frequency ($\omega$). Given the wave equations in the form $y = a \sin(\omega t + \phi)$, the angular frequency is the coefficient of $t$.

  • Wave (i): $\omega_1 = \omega$
  • Wave (ii): $\omega_2 = 2\omega$
  • Wave (iii): $\omega_3 = 2\omega$
  • Wave (iv): $\omega_4 = 4\omega$

Step 2 (Step-by-Step Mathematical Working): [1 Mark]

We evaluate the pairs provided in the options based on the condition $\omega_a = \omega_b$:

  • (A) (i) and (ii): $\omega_1 = \omega$ and $\omega_2 = 2\omega$. Since $\omega \neq 2\omega$, they cannot produce interference.
  • (B) (ii) and (iii): $y_2 = a \sin(2\omega t)$ and $y_3 = a \sin(2\omega t + \phi)$. Here, both waves have the same angular frequency $2\omega$ and a constant phase difference $\phi$.
  • (C) (iii) and (iv): $\omega_3 = 2\omega$ and $\omega_4 = 4\omega$. Since $2\omega \neq 4\omega$, they cannot produce interference.
  • (D) (iv) and (i): $\omega_4 = 4\omega$ and $\omega_1 = \omega$. Since $4\omega \neq \omega$, they cannot produce interference.

Step 3 (Final Concluded Answer): [1 Mark]

Since only pair (ii) and (iii) possess the same angular frequency, they satisfy the condition for coherence. Therefore, the correct option is (B).

💡 EL10 Concept Insight: Think of interference like two people singing a note; if they sing at different pitches (frequencies), the sound just clashes and sounds messy. To get a steady, rhythmic "interference" pattern, they must sing the exact same note at the same pitch so their sound waves can perfectly overlap and reinforce or cancel each other out.

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