Answer:
The correct answer is "4.26 m".
Explanation:
Given:
Wavelength,
[tex]\lambda = 436.1 \ nm[/tex]
or,
[tex]=436.1\times 10^{-9} \ m[/tex]
Distance,
[tex]d = 0.31 \ mm[/tex]
or,
[tex]=0.31\times 10^{-3} \ m[/tex]
Distance between the 1st and 2nd dark fringes,
[tex](y_2-y_1) = 6\times 10^{-3} \ m[/tex]
As we know,
⇒ [tex]\frac{d}{L} (y_2-y_1) = \lambda[/tex]
or,
⇒ [tex]L=\frac{d(y_2-y_1)}{\lambda}[/tex]
By substituting the values, we get
[tex]=\frac{0.31\times 6\times 10^{-6}}{436.1\times 10^{-9}}[/tex]
[tex]=\frac{0.31\times 6\times 10^3}{436.1}[/tex]
[tex]=\frac{1860}{436.1}[/tex]
[tex]=4.26 \ m[/tex]
