Answer:
[tex]\lambda=5.60\times 10^{-5}\ m[/tex]
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]
For two fringes:
The formula is:
[tex]\Delta y=L\times \frac {\lambda}{d}\times \Delta m[/tex]
For first and second bright fringe,
[tex]\Delta m=1[/tex]
Given that:
[tex]\Delta y=0.024\ m[/tex]
d = 2.80 mm
L = 1.20 m
Also,
1 mm = 10⁻³ m
d = 2.80×10⁻³ m
Applying in the formula,
[tex]0.024=1.20\times \frac {\lambda}{2.80\times 10^{-3}}\times 1[/tex]
[tex]\lambda=5.60\times 10^{-5}\ m[/tex]
