Q. Given below are two statements :
Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength
In the light of the above statements, choose the correct answer from the options given below :
A. Both Statement I and Statement II are true
B. Statement I is true but Statement II is false
C. Statement I is false but Statement II is true
D. Both Statement I and Statement II are false
Explanation
In Young's double slit experiment, angular fringe separation is given by
\[
\theta = \frac{\lambda}{d}
\]
where \( \lambda \) is wavelength and \( d \) is slit separation.
Angular separation depends only on wavelength and slit separation. It does not depend on the distance of screen from the slits.
Hence, moving the screen away does not change angular separation. Therefore, Statement I is false.
If wavelength increases, then
\[
\theta \propto \lambda
\]
So angular separation increases. Therefore, Statement II is true.
Hence the correct option is Statement I is false but Statement II is true.