MHT CET · Physics · Wave Optics
Two identical light waves having phase difference \(\phi\) propagate in same direction. When they superpose, the intensity of resultant wave is proportional to
- A \(\cos ^2\left(\frac{\phi}{4}\right)\)
- B \(\cos ^2\left(\frac{\phi}{3}\right)\)
- C \(\cos ^2\left(\frac{\phi}{2}\right)\)
- D \(\cos ^2 \phi\).
Answer & Solution
Correct Answer
(C) \(\cos ^2\left(\frac{\phi}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(A^2=a_1^2+a_i^2+2 a_1 a_2 \cos \phi\), where \(A\) is amplitude of resultant wave and given that, \(a_1=a_2=a\), where, a is amplitude of individual wave.
\(\begin{array}{ll}
\therefore \quad & A^2=2 a^2(1+\cos \phi)=2 a^2\left(1+2 \cos ^2 \frac{\phi}{2}-1\right) \\
& \Rightarrow A^2 \propto \cos ^2 \cdot \frac{\phi}{2}
\end{array}\)
Now, \(I \propto \mathrm{~A}^2\)
\(\therefore \quad I \propto A^2 \propto \cos ^2 \frac{\phi}{2} \Rightarrow I \propto \cos ^2 \frac{\phi}{2}\)
\(\begin{array}{ll}
\therefore \quad & A^2=2 a^2(1+\cos \phi)=2 a^2\left(1+2 \cos ^2 \frac{\phi}{2}-1\right) \\
& \Rightarrow A^2 \propto \cos ^2 \cdot \frac{\phi}{2}
\end{array}\)
Now, \(I \propto \mathrm{~A}^2\)
\(\therefore \quad I \propto A^2 \propto \cos ^2 \frac{\phi}{2} \Rightarrow I \propto \cos ^2 \frac{\phi}{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- In Bohr's theory of Hydrogen atom, the electron jumps from higher orbit \(n\) to lower orbit \(p\). The wavelength will be maximum for the transitionMHT CET 2016 Easy
- An electron of mass ' \(m\) ' and a photon have same energy ' \(E\) '. The ratio of de-Broglie wavelength of electron to the wavelength of photon is \((\mathrm{c}=\) velocity of light \()\)MHT CET 2021 Hard
- In a single slit diffraction experiment, for a wavelength of light ' \(\lambda\) ', half-angular width of the principle maxima is ' \(\theta\) '. Also for wavelength of light \(\mathrm{p} \lambda\), the half angular width of the principle maxima is \(q \theta\). The ratio of the halfangular widths of the first secondary maxima in the first case to second case will beMHT CET 2024 Easy
- The side of a copper cube is \(1 \mathrm{~m}\) at \(0^{\circ} \mathrm{C}\). What will be the change in its volume, when it is heated to \(100^{\circ} \mathrm{C}\) ? \(\left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]\)MHT CET 2023 Medium
- The acceleration (a) - time (T) graph for the body starting from rest is given below. The maximum speed of the body is
MHT CET 2025 Medium - Maximum kinetic energy gained by the charged particle in the cyclotron is independent ofMHT CET 2019 Medium
More PYQs from MHT CET
- If \(\bar{a}\) and \(\overline{\mathrm{b}}\) are unit vectors and \(\theta\) is the angle between them, then \(\tan \theta / 2=\)MHT CET 2025 Medium
- Time is a crucial factor for ________.MHT CET 2025 Medium
- A Carnot engine has efficiency \(\frac{1}{6}\). It becomes \(\frac{1}{3}\), when the temperature of sink is lowered by 57 K . The temperature of the source isMHT CET 2025 Medium
- Average power in the \(L-C-R\) circuit depends uponMHT CET 2010 Easy
- The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted areMHT CET 2021 Easy
- What are the products obtained when water is auto-photolysed?MHT CET 2018 Medium