Step 1: Find the distance of the third bright fringe on the screen from the central maximum.
The wavelength of the light beam, λ_1​ = 650 nm
The wavelength of another light beam, λ₂​ = 520 nm
The distance of the slits from the screen = D
Distance between the two slits = d
\(x=n\lambda _{1}\left ( \frac{D}{d} \right )\)
For the third bright fringe, n=3
\(\Rightarrow x=3\times 650\left ( \frac{D}{d} \right )=1950\left ( \frac{D}{d} \right )~nm.\)

(b)
Hint: \(x=n\lambda _{2}\left ( \frac{D}{d} \right )\)

Step 1: Equate the conditions for bright fringes.
\(n\lambda _{2}=\left ( n-1 \right )\lambda _{1}\)
\(\Rightarrow~520n=650n-650~\Rightarrow n=5 \)
Step 2: Find the least distance from the central maximum.
\(x=n\lambda _{2}\left ( \frac{D}{d} \right )=5\times520\left ( \frac{D}{d} \right )=2600\left ( \frac{D}{d} \right )~nm.\)
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