Optics Question 172
Question: White light may be considered to be a mixture of waves with l ranging between $ 3900{AA} $ and $ 7800{AA} $ . An oil film of thickness $ 10,000{AA} $ is examined normally by reflected light. If m = 1.4, then the film appears bright for
Options:
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} $
Show Answer
Answer:
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.
