Answer:
632 nm
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=1.58\ cm[/tex]
d = 0.200 mm
L = 5.00 m
Also,
1 cm = 10⁻² m
1 mm = 10⁻³ m
So,
[tex]\Delta y=1.58\times 10^{-2}\ m[/tex]
d = 0.2×10⁻³ m
Applying in the formula,
[tex]1.58\times 10^{-2}=5.00\times \frac {\lambda}{0.2\times 10^{-3}}\times 1[/tex]
[tex]\lambda=632\times 10^{-9}\ m[/tex]
Also,
1 m = 10⁹ nm
So wavelength is 632 nm
