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(D) The formula for fringe width is $\beta = \frac{D \lambda}{d}$,where $D$ is the distance between the screen and the slits,$\lambda$ is the waveleng

Vedclass · Accepted Answer

$0.3$

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(D) The formula for fringe width is $\beta = \frac{D \lambda}{d}$,where $D$ is the distance between the screen and the slits,$\lambda$ is the wavelength,and $d$ is the slit separation.Given for the first case:$\lambda_1 = 5000 \,\mathring A$,$d_1 = d$,$\beta_1 = 0.5 \,mm$.So,$\beta_1 = \frac{D \lambda_1}{d} = 0.5 \,mm$ ... $(I)$For the second case:$\lambda_2 = 6000 \,\mathring A$,$d_2 = 2d$,$\beta_2 = ?$So,$\beta_2 = \frac{D \lambda_2}{d_2} = \frac{D 	imes 6000 \,\mathring A}{2d}$ ... $(II)$Dividing $(II)$ by $(I)$:$\frac{\beta_2}{\beta_1} = \frac{D 	imes 6000 \,\mathring A / 2d}{D 	imes 5000 \,\mathring A / d} = \frac{6000}{2 	imes 5000} = \frac{6}{10} = 0.6$Therefore,$\beta_2 = 0.6 	imes \beta_1 = 0.6 	imes 0.5 \,mm = 0.3 \,mm$.

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