Answer:
"6.67 mm" is the right solution.
Explanation:
The given values are:
As we know, the equation
⇒ [tex]\frac{y}{L} =\frac{x \lambda}{a}[/tex]
On substituting the values, we get
⇒ [tex]\frac{.0125}{2.5}=\frac{(1)(600\times 10^{-9}) }{a}[/tex]
On applying cross multiplication, we get
⇒ [tex].0125a=2.5 (600\times 10^{-9})[/tex]
⇒ [tex]a=\frac{2.5(600\times 10^{-9})}{.0125}[/tex]
⇒ [tex]=1.2\times 10^{-4} \ m[/tex]
For new distance, we have to put this value of "a" in the above equation,
⇒ [tex]\frac{y}{1.5} =\frac{(1)(600\times 10^{-9})}{1.2\times 10^{-4}}[/tex]
⇒ [tex](1.2\times 10^{-4})y=1.5(600\times 10^{-9})[/tex]
⇒ [tex]y=\frac{1.5(600\times 10^{-9})}{1.2\times 10^{-4}}[/tex]
⇒ [tex]=3.22\times 10^{-3} \ m[/tex]
The total distance will be twice the value of "y", we get
= [tex]6.67\times 10^{-3} \ m[/tex]
or,
= [tex]6.67 \ mm[/tex]
