Answer:
final displacement = +24484.5 nm
Explanation:
The path difference when 158 bright spots were observed with red light (λ1 = 656.3 nm) is given as;
Δr = 2d2 - 2d1 = 150λ1
So, 2d2 - 2d1 = 150λ1
Dividing both sides by 2 to get;
d2 - d1 = 75λ1 - - - - eq1
Where;
d1 = distance between the fixed mirror and the beam splitter
d2 = position of moveable mirror from splitter when 158 bright spots are observed
Now, the path difference between the two waves when 114 bright spots were observed is;
Δr = 2d'2 - 2d1 = 114λ1
2d'2 - 2d1 = 114λ1
Divide both sides by 2 to get;
d'2 - d1 = 57λ1
Where;
d'2 is the new position of the movable mirror from the splitter
Now, the displacement of the moveable mirror is (d2 - d'2). To get this, we will subtract eq2 from eq1.
(d2 - d1) - (d'2 - d1) = 75λ1 - 57λ2
d2 - d1 - d'2 + d1 = 75λ1 - 57λ2
d2 - d'2 = 75λ1 - 57λ2
We are given;
(λ1 = 656.3 nm) and λ2 = 434.0 nm.
Thus;
d2 - d'2 = 75(656.3) - 57(434)
d2 - d'2 = +24484.5 nm
