A) \[4308\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ }5091\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ }6222\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ }5091\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 5600}\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[4667\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 6222}\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 7000}\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 4667}\overset{\text{o}}{\mathop{\text{A}}}\,,\text{ 5600}\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,70\text{00}\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: A
Solution :
The film appears bright if the path difference is \[2\mu t\cos r=(2n-1)\frac{\lambda }{2}\] \[n=1,2,3...\] \[\therefore \]\[\lambda =\frac{4\mu t\cos r}{(2n-1)}\] \[\lambda =\frac{4\times 1.4\times 10000\times {{10}^{-10}}\cos {{0}^{o}}}{(2n-1)}\] \[=\frac{56000}{(2n-1)}{AA}\] \[\therefore \]\[\lambda =56000{AA},\text{ }18666{AA},\text{ }11200{AA},\text{ }8000{AA},\] \[6222{AA},\text{ }5091{AA},\text{ }4308{AA},\text{ }3733{AA}\] The wavelengths which are not within specified ranges are to be rejected.
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