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(C) The fringe width $\beta$ in a Young's double-slit experiment is given by the formula $\beta = \frac{\lambda D}{d}$.Since the experimental setup ($

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$1.2$

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(C) The fringe width $\beta$ in a Young's double-slit experiment is given by the formula $\beta = \frac{\lambda D}{d}$.Since the experimental setup ($D$ and $d$) remains unchanged,the fringe width is directly proportional to the wavelength of light: $\beta \propto \lambda$.Therefore,$\frac{\beta_2}{\beta_1} = \frac{\lambda_2}{\lambda_1}$.Given: $\beta_1 = 1.0 \ mm$,$\lambda_1 = 5000 \ \mathring{A}$,and $\lambda_2 = 6000 \ \mathring{A}$.Substituting the values: $\beta_2 = \beta_1 	imes \frac{\lambda_2}{\lambda_1} = 1.0 	imes \frac{6000}{5000} = 1.2 \ mm$.Thus,the new fringe width is $1.2 \ mm$.

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