The optical path difference between two identical light waves arriving at a point (P) on the screen is `27xx10^(-7)m`. For P to be a dark point, the wavelength of light used should be

Options

A. 3000 Å
B. 4000 Å
C. 5000 Å
D. 6000 Å

Answer

D

Explanation

Path difference`=27xx10^(-7)m`
for P is be a dark point, it must be an odd multiple of `lamda/2`
(i) if `lamda=3000` Å`=3xx10^(-7)`m
then `(27xx10^(-7))/(3xx10^(-7))=9`. It is bright point
(ii) for `lamda=4xx10^(-7),("Path difference")/(lamda)=(27)/(4)`
(iii) for `lamda=5000` Å, `("Path difference")/(lamda)=(27)/(5)` ltBrgt i.e. (i) (ii) and (iii) cannot give a dark point
for `lamda=6000` Å, `("path difference")/(lamda)=(27)/(6)=(9)/(2)`
this is an odd multiple of `lamda/2`
`therefore lamda` should be 6000 Å