A) \[6000{{A}^{o}}\]
B) \[5000{{A}^{o}}\]
C) \[3000{{A}^{o}}\]
D) \[4500{{A}^{o}}\]
Correct Answer: A
Solution :
\[\beta =\frac{\lambda D}{d}\] \[\Rightarrow \] \[\beta \propto D\] \[\Rightarrow \] \[\frac{{{\beta }_{1}}}{{{\beta }_{2}}}=\frac{{{D}_{1}}}{{{D}_{2}}}\] \[\Rightarrow \] \[\frac{{{\beta }_{1}}-{{\beta }_{2}}}{{{\beta }_{2}}}=\frac{{{D}_{1}}-{{D}_{2}}}{{{D}_{2}}}\] \[\Rightarrow \] \[\frac{\Delta \beta }{\Delta D}=\frac{{{\beta }_{2}}}{{{D}_{2}}}=\frac{{{\lambda }_{2}}}{{{d}_{2}}}\] \[\Rightarrow \] \[{{\lambda }_{2}}=\frac{3\times {{10}^{-5}}}{5\times {{10}^{-2}}}\times {{10}^{-3}}\] \[=6\times {{10}^{-7}}m\] \[=6000{\AA}\]
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