Answer:
6.9066 × 10⁻⁵ m
Explanation:
For constructive interference, the expression is:
[tex]d\times sin\theta=m\times \lambda[/tex]
Where, m = 1, 2, .....
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]
Thus, the distance between the central maximum is 3.00 cm
First bright fringe , m = 1 occur at 3.00 / 2 = 1.50 cm
Since,
1 cm = 0.01 m
y = 0.0150 m
Given L = 2.00 m
λ = 518 nm
Since, 1 nm = 10⁻⁹ m
So,
λ = 518 × 10⁻⁹ m
Applying the formula as:
[tex]0.0150\ m=2.00\ m\times \frac {518\times 10^{-9}\ m}{d}\times 1[/tex]
⇒ d, distance between the slits = 6.9066 × 10⁻⁵ m
