Answer:
The value is [tex]\lambda = 900 \ nm[/tex]
Explanation:
From the question we are told that
The width of the slit is [tex]a = 0.15 \ mm = 0.00015 \ m[/tex]
The distance of the screen from the slit is D = 1.25 m
The width of the central maximum is [tex]y = 0.75 \ cm = 0.0075 \ m[/tex]
Generally the width of the central maximum is mathematically represented as
[tex]y = \frac{m * D * \lambda}{a}[/tex]
Here m is the order of the fringe and given that we are considering the central maximum, the order will be m = 1 because the with of the central maximum separate's the and first maxima
So
[tex]\lambda = \frac{a y}{ m * D }[/tex]
=> [tex]\lambda = \frac{ 0.000015 * 0.0075}{ 1 * 1.2 }[/tex]
=> [tex]\lambda = 900 *10^{-9} \ m[/tex]
=> [tex]\lambda = 900 \ nm[/tex]
