Given below are two statements : one is labelled as Assertion (A)...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below :

Options

ABoth $(\mathbf{A})$ and $(\mathbf{R})$ are true but $(\mathbf{R})$ is not the correct explanation of $(\mathbf{A})$
BBoth $(\mathbf{A})$ and $(\mathbf{R})$ are true and $(\mathbf{R})$ is the correct explanation of $(\mathbf{A})$
C(A) is true but (R) is false
D $(A)$ is false but (R) is true

Correct answer

B. Both $(\mathbf{A})$ and $(\mathbf{R})$ are true and $(\mathbf{R})$ is the correct explanation of $(\mathbf{A})$

Step-by-step solution

\beta(\text{ fringe width })=\frac{\lambda D}{d}

In denser medium,

\lambda \downarrow \Rightarrow \beta \downarrow \Rightarrow

fringe come closer Also,

\mu=\frac{\mathrm{c}}{\mathrm{V}} \Rightarrow \mathrm{V}=\frac{\mathrm{c}}{\mu}

Frequency remains same,

\Rightarrow \mu=\frac{\lambda_{\mathrm{vac} .} \mathrm{f}}{\lambda_{\mathrm{med}} \mathrm{f}} \Rightarrow \lambda_{\mathrm{med}}=\frac{\lambda_{\mathrm{vac} .}}{\mu}

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