A two-slit arrangement with 60.3 μm separation between the slits is illuminated with $491.0 \mathrm {~nm}$ coherent light. If a viewing screen is located 2.14 m from the slits, find the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.
A) 52.3 mm
B) 34.9 mm
C) 69.7 mm
D) 24.6 mm

Question

Quizplus · Accepted Answer

The distance between the two slits is given as 60.3 μm, i.e. 0.0603 mm. The wavelength of the light is given as $\lambda = 491.0 \mathrm{~nm}$. The distance from the slits to the viewing screen is given as 2.14 m.

We can use the formula for the position of the nth dark fringe:

$$ x_n =\frac{n\lambda D}{d} $$

where n is the order of the fringe, λ is the wavelength of the light, D is the distance from the slits to the viewing screen, and d is the distance between the two slits.

For the first dark fringe on one side of the central maximum, we take n = 1. For the second dark fringe on the other side, we take n = 2. Substituting the given values, we get:

$$ x_1 =\frac{1\times 491.0\times 2.14}{0.0603} = 17339 \mathrm{~\mu m}= \mathrm{17.339 ~mm} $$

and

$$ x_2 =\frac{2\times 491.0\times 2.14}{0.0603} = 34678 \mathrm{~\mu m}= \mathrm{34.678 ~mm} $$

The distance between the first and second dark fringes is:

$$ x_2 - x_1 = 34.678 - 17.339 = 17.339 \mathrm{~mm} $$

Therefore, the best choice is B with a distance of 34.9 mm.

A Two-Slit Arrangement with 60 491.0 nm491.0 \mathrm {~nm}491.0 nm Coherent Light

A Two-Slit Arrangement with 60 $491.0 \mathrm {~nm}$ Coherent Light