A) \[0.9\] mm
B) \[0.8\] mm
C) \[1.8\] mm
D) \[1.6\] mm
Correct Answer: B
Solution :
Young's double slit interference experiment,\[b=\frac{\lambda D}{d}\] Given \[{{\beta }_{1}}=1.2\ mm\]\[\frac{{{d}_{2}}}{{{d}_{1}}}=1\,\frac{1}{2}\,=1.5\] So, \[\beta \propto \,\frac{1}{d}\Rightarrow \,\frac{{{\beta }_{1}}}{{{\beta }_{2}}}\,=\frac{1/{{d}_{1}}}{1/{{d}_{2}}}\Rightarrow \,\frac{{{\beta }_{1}}}{{{\beta }_{2}}}\,=\frac{{{d}_{1}}}{{{d}_{2}}}=1.5\] \[\Rightarrow \,\frac{1.2}{{{\beta }_{2}}}\,=1.5\Rightarrow \,{{\beta }_{2}}=\frac{1.2}{1.5}=\frac{4}{5}=0.8mm\]
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