Complete Question
A student locates a double-slit assembly 1.40 m from a reflective screen. The slits are separated by 0.0572 mm.
(a) Suppose the student aims a beam of yellow light, with a wavelength of 589 nm, toward the slit assembly, and this makes an interference pattern on the screen. What distance (in cm) separates the zeroth-order and first-order bright fringes (a.k.a. maxima)?
(b)
Now suppose that blue light (with
λ = 415 nm)
is used instead. What distance (in cm) will now separate the second-order and fourth-order bright fringes?
Answer:
a
The distance of separation is
b
The distance of separation is
Explanation:
From the question we are told that
The distance from the screen is
The slit separation is
The wavelength of the yellow light is
The distance of a fringe from the central maxima is mathematically represented as
Where n is the order of the fringe so the distance of separation between
The distance that separates first order from zeroth order bright fringe can be evaluated as
Substituting values
Converting to cm
b
The wavelength of blue light is
So the distance that separates second order from fourth order bright fringe can be evaluated as
Substituting values
Converting to cm