Answer:
200 nodal lines
Explanation:
To find the number of lines you first use the following formula for the condition of constructive interference:
[tex]dsin\theta=m\lambda[/tex] (1)
d: distance between slits = 0.1mm = 0.1*10^-3 m
θ: angle between the axis of the slits and the m-th fringe of interference
λ: wavelength of light = 400 nm = 400*10^-9 m
You obtain the max number of lines when he angle is 90°. Then, you replace the angle by 90° and solve the equation (1) for m:
[tex]dsin90\°=m\lambda\\\\d=m\lambda\\\\m=\frac{d}{\lambda}=\frac{0.1*10^{-3}m}{500*10^{-9}m}=200[/tex]
hence, the number of lines in the interference pattern are 200
