In the young's double slit experiment, the intensity of light at a point on the screen (where the path difference is $straight lambda$ ) is K. The intensity at a point where the path difference is $bevelled straight lambda over 4$ will be,

K

K/4

K/2

zero

Solution

K/2

For net intensity,
I' = 4 I_o cos² $straight ϕ over 2$ $open parentheses straight ϕ space equals fraction numerator 2 straight pi over denominator straight lambda end fraction xλ close parentheses$
For the first case,
K = 4 I_o cos² $straight pi$
K = 4 I_o ... (i)
For the second case,
$straight K apostrophe space equals space 4 straight I subscript straight o space cos squared open parentheses fraction numerator begin display style bevelled straight pi over 2 end style over denominator 2 end fraction close parentheses space open parentheses straight ϕ equals fraction numerator 2 straight pi over denominator straight lambda end fraction straight x straight lambda over 4 close parentheses space space space space equals space 4 space straight I subscript straight o space cos squared space left square bracket straight pi divided by 2 right square bracket space space space space equals space 2 straight I subscript straight o$ ... (ii)
Comparing equations (i) and (ii), we have
K' = K/2