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(D) The fringe width $\beta$ in Young's double slit experiment is given by the formula $\beta = \frac{\lambda D}{d}$,where $\lambda$ is the wavelength

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The separation between successive dark fringes remains unchanged

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(D) The fringe width $\beta$ in Young's double slit experiment is given by the formula $\beta = \frac{\lambda D}{d}$,where $\lambda$ is the wavelength,$D$ is the distance between the screen and the slits,and $d$ is the separation between the slits.Given that the wavelength $\lambda$ is changed from $7000 \ \mathring{A}$ to $3500 \ \mathring{A}$ (halved) and the slit separation $d$ is doubled $(d' = 2d)$,the new fringe width $\beta'$ becomes:$\beta' = \frac{(\lambda/2) D}{2d} = \frac{1}{4} \frac{\lambda D}{d} = \frac{1}{4} \beta$.Since the fringe width changes,the separation between successive bright fringes and successive dark fringes (which is equal to the fringe width) also changes.Therefore,the statement that the separation between successive dark fringes remains unchanged is false.

In Young's double slit experiment,the wavelength of light was changed from $7000 \ \mathring{A}$ to $3500 \ \mathring{A}$. While doubling the separation between the slits,which of the following is not true for this experiment?

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