Coherent sources and their importance in interference

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Question

In an Interference pattern of Young’s double slit experiment, we observe the 12th order maxima for wavelength 600 nm at a point on the screen. What order maxima will be visible at the same point, if the source is replaced by light of wavelength 480 nm.

Moderate

Solution

$Δ x = \frac{y d}{D} = m_{1} λ_{1} = m_{2} λ_{2} ∴ \frac{m_{1}}{m_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{480}{600} = \frac{48}{60} \Rightarrow \frac{12}{m_{2}} = \frac{48}{60} ∴ m_{2} = \frac{12 \times 60}{48} = 15 t h$

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