A parrallel beam of light `(lambda=5000Å)` is incident at an angle `alpha=30^(@)` as shown in YDSE experiment. Intensity due to each slit at any point on screen in `I_(0)`. The distance between slits is 1mm. The intensity at central point O on the screen is `KI_(0)`. Find the value of K.

Options

A. the intensity at O is `4 I_(0)`
B. the intensity at is zero
C. the intensity at a point on the screen 1 m below O is `4 I_(0)`
D. the intensity at a point on the screen 1 m below O is zero

Answer

a.,c

Explanation

Path difference at point `O = d sin alpha = 0.5 mm`
Corresponding phase difference,
`Delta phi = (2pi)/(lambda) xx Delta x`
`= (2 pi (0.5 xx 10^(-3)))/(5000 xx 10^(-10)) = 2000 pi = 2 pi xx 1000`
O is point corresponding to a maxima with the point at 1m below O corresponding to central maixma.