A) \[4308\,\,{AA},\,\,5091\,\,{AA},\,\,6222\,\,{AA}\]
B) \[4000\,\,{AA},\,\,5091\,\,{AA},\,\,5600\,\,{AA}\]
C) \[4667\,\,{AA},\,\,6222\,\,{AA},7000\,\,{AA}\]
D) \[4000\,\,{AA},\,\,4667\,\,{AA},\,\,5600\,\,{AA},\,\,7000\,\,{AA}\]
Correct Answer: A
Solution :
The film appears bright when the path difference \[(2\mu \,t\,\cos r)\] is equal to odd multiple of \[\frac{\lambda }{2}\] i.e. \[2\mu t\cos r=(2n-1)\ \lambda /2\] where \[n=1,\,\,2,\,\,3\,\,.....\] \[\therefore \,\,\,\lambda =\frac{4\mu \,t\,\cos r}{(2n-1)}\] \[=\frac{4\times 1.4\times 10,000\times {{10}^{-10}}\times \cos 0}{(2n-1)}=\frac{56000}{(2n-1)}{AA}\] \[\therefore \,\,\lambda =56000\,{AA}\] \[18666\,{AA},\] \[8000\,{AA},\] \[6222\,{AA},\] \[5091\,{AA},\] \[4308\,{AA},\] \[3733\,{AA}.\] The wavelength which are not within specified range are to be refracted.
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