The angular width of a fringe in a double sli | vedclass

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Question

(A) The angular fringe width $\beta_{	heta}$ is given by the formula $\beta_{	heta} = \frac{\lambda}{d}$, where $\lambda$ is the wavelength of light

Vedclass · Accepted Answer

$0.05$

Vedclass · Answer

(A) The angular fringe width $\beta_{	heta}$ is given by the formula $\beta_{	heta} = \frac{\lambda}{d}$, where $\lambda$ is the wavelength of light and $d$ is the slit separation.Since $\beta_{	heta} \propto \lambda$, when the system is immersed in water, the wavelength changes to $\lambda' = \frac{\lambda}{\mu}$.Therefore, the new angular width $\beta_{	heta}'$ is $\beta_{	heta}' = \frac{\beta_{	heta}}{\mu}$.Given $\beta_{	heta} = 0.2^{\circ}$ and $\mu = \frac{4}{3}$, the new angular width is $\beta_{	heta}' = 0.2^{\circ} 	imes \frac{3}{4} = 0.15^{\circ}$.The change in angular width is $\Delta \beta_{	heta} = \beta_{	heta} - \beta_{	heta}' = 0.2^{\circ} - 0.15^{\circ} = 0.05^{\circ}$.

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