In the young's double slit experiment, the intensities at two points `P(1)` and `P_(2)` on the screen are respectively `I_(1)` and `I_(2)`. If `P_(1)` is located at the centre of a bright fringe and `P_(2)` is located at a distance equal to a quarter of fringe width from `P_(1)`, then `I_(1)/I_(2)` is

Options

A. 2
B. `1/2`
C. 4
D. 16

Answer

a

Explanation

If the amplitude of interfering wave is 'a' then the intensity at any point is given by,
`I_(1)=4a^(2)cos^(2)(phi/2)`
`I_(1)=4a^(2)(because cos^(2)(phi/2)=1) …….(1)`
`I_(2)=4a^(2)cos^(2)(pi/4)`
`=2a^(2) ….(2)`
`I_(1)/I_(2)=(4a^(2))/(2a^(2))`
`therefore I_(1)/I_(2)=2`