Answer:
The wavelength will be "1.182 μm".
Explanation:
The given values are:
Wavelength
[tex]\lambda=591 \ nm[/tex]
or,
[tex]=591\times 10^-9 \ m[/tex]
Distance,
[tex]d = 3.00 m[/tex]
[tex]n = 1[/tex]
Distance of fringe from center,
[tex]y = 4.84 \ mm[/tex]
We have to find the wavelength of first order dark fringe,
[tex]\lambda = ?[/tex]
As we know,
⇒ [tex]y_{bright} =\frac{1\times \lambda\times L}{d}[/tex]
On putting the given values in the formula, we get
[tex]0.00484=\frac{1\times (591\times 10^{-9})\times 3}{d}[/tex]
On applying the cross multiplication, we get
[tex]\lambda = \frac{0.00484\times 000036632}{0.5\times 3}[/tex]
[tex]=1182\times 10^{-9}[/tex]
or,
[tex]=1.182 \ \mu m[/tex]
