Bichromatic light is used in YDSE having wavelengths `lambda_(1)=400nm` and `lambda_(2)=700nm` Find minimum order of `lambda_(1)` which overlaps with `lambda_(2)`

Explanation

(a) The condition for a minima in a single-slit diffraction pattern is given by
`asintheta=nlambda`
where a is the slit width, is the wavelength, and n is the integer. For `lambda=lambda_(1)`  and n = 1, the value of sin is same as for `lambda=lambda_(2)`and  n= 2. Thus, `sintheta=(lambda_(1))/(a)=(2lambda_(2))/(a)`
or `lambda_(1)=2lambda_(2)`
(b) A minimum in one pattern coincides with a minimum in the other if they occur at the same angle. This means that
`m_(1)lambda_(1)=lambda_(2)m_(2)`
where `m_(1)` and `m_(2)` ane integers associated with a minimum in pattern corresponding the wavelength `lambda_(1)`and `lambda_(2)` , respectively: Since `lambda_(1)=2lambda_(2)`,, the minima coincide if `2m_(1) = m_(2)`. thus every other minimum of the pattern coincides with a minimum of the`lambda_(1)` pattern.