In Young's interfernce experiment has a set up as shown in figure, consider that a source of monochromatic light of wavelength 5000Å is placed at `S.S_(1)` and `S_(2)` are equidistant from S and have equal widths. A wvefront, eit light waves, which superimpose to result in an interference pattern on the screen kept at position (1). this is an experiment where coherent sources are obtained by division of wavefront. O is a point on the screen equidistant from `S_(1) and S_(2)`. P is a point on the screen 1 mm from O at which path difference between waves from `S_(1) and S_(2)` is 11250Å. Position of amy point on the screen can be expressed by `theta`. The path difference is zero at O and a central bright fringe of intensity `I_(0)` is obtained at O. Q is another point 2 mm from O. If the screen is now shifted to a new position (2) [not shown in figure] so that D changes, the fringe width is found to be 50% more than its earlier value and the angular fringe width is `(1)/(90)` radian. Answer the following question [assume D to be large and `theta` very small so taht `sinapproxtantheta approxtheta`]
Q. Angular position of a bright fringe of order 5 when the screen is at position (1), will be nearly

Options

A. `(1)/(9)rad`
B. `(1)/(18)rad`
C. `(1)/(10)rad`
D. none of these

Answer

B