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(B) Conditions for sustained interference of light: $(i)$ The sources must be coherent. $(ii)$ The sources must be monochromatic.The fringe width is g

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$3$

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(B) Conditions for sustained interference of light: $(i)$ The sources must be coherent. $(ii)$ The sources must be monochromatic.The fringe width is given by $\beta = \frac{\lambda D}{d}$.For the first case: $\beta_1 = \frac{\lambda_1 D_1}{d_1}$,where $\lambda_1 = 400 \, nm$.For the second case: $\beta_2 = \frac{\lambda_2 D_2}{d_2}$,where $\lambda_2 = 600 \, nm$ and $d_2 = \frac{d_1}{2}$.Given that the fringe width remains the same,$\beta_1 = \beta_2$:$\frac{\lambda_1 D_1}{d_1} = \frac{\lambda_2 D_2}{d_2}$$\frac{D_1}{D_2} = \frac{\lambda_2 d_1}{\lambda_1 d_2} = \frac{600}{400} 	imes \frac{d_1}{d_1/2} = \frac{3}{2} 	imes 2 = 3$.Thus,the ratio of the distances is $3:1$.

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