Answer :
Answer:
5.81 × 10⁻⁵ m
Explanation:
For constructive interference, the expression is:
[tex]d\times sin\theta=m\times \lambda[/tex]
d is the distance between the slits.
The formula can be written as:
[tex]sin\theta=\frac {\lambda}{d}\times m[/tex] ....1
The location of the bright fringe is determined by :
[tex]y=L\times tan\theta[/tex]
Where, L is the distance between the slit and the screen.
For small angle , [tex]sin\theta=tan\theta[/tex]
So,
Formula becomes:
[tex]y=L\times sin\theta[/tex]
Using 1, we get:
[tex]y=L\times \frac {\lambda}{d}\times m[/tex]
Given that:
m = 3, y = 47 mm (Location of the fringe)
Since,
1 mm = 0.001 m
y = 0.047 m
Given L =1.4 m
λ = 650 nm
Since, 1 nm = 10⁻⁹ m
So,
λ = 650 × 10⁻⁹ m
Applying the formula as:
[tex]0.047\ m=1.4\ m\times \frac {650\times 10^{-9}\ m}{d}\times 3[/tex]
⇒ d, distance between the slits = 5.81 × 10⁻⁵ m