Correct Answer - Option 1 : 25
The correct answer is option 1) i.e. 25
CONCEPT:
-
Coherent sources: Two sources are coherent if the waves from these sources have the same frequency and same phase difference.
- For a given wave, its wavelength (λ), frequency (f), and speed of light in a vacuum (c) are related as follows:
\(λ =\frac{c}{f}\)
- Phase difference is the difference in the phase angle between two waves.
- Path difference is the difference in the path traversed by the two waves.
- The phase difference (Δϕ) and path difference (Δx) for any two waves of the same frequency is given by:
\(\Rightarrow Δ x=\frac{λ } {2\pi }× Δ ϕ\)
Where λ is the wavelength of the waves.
CALCULATION:
Given that:
Wavelength of the waves, λ = 6280 A° = 6280 × 10-10 m
Path difference, Δx = 2.5 micron = 2.5 × 10-6 m
We know,
\(\Rightarrow λ =\frac{c}{f} \Rightarrow \lambda \propto \frac{1}{f}\) (∵ speed of light is a constant value)
- Therefore, if two given waves have the same wavelength and phase difference, they will have the same frequency and can be considered as coherent sources.
Using the relation,
\(\Rightarrow Δ x=\frac{λ } {2\pi }× Δ ϕ\)
\(\Rightarrow 2.5 \times 10^{-6} =\frac{6280 × 10^{-10}} {2\pi } \times \Delta\phi\)
\(\Rightarrow \Delta\phi = \frac{2.5 \times 10^{-6} \times 2\pi }{6280 × 10^{-10}} = 25\: radian\)
