Question

A diffraction experiment involving two thin parallel slits yields a pattern of closely spaced bright and dark fringes on a screen placed 2.35 m away.In the central part of the pattern, a student observes 7 bright spots equally spaced at 1.05 mm from center to center. The light source was a coherent source of wavelength 438 nm.Both answers below should be expressed in micrometers 

Answer 1

To find the slit separation (d) and the width of each slit (w) in the double-slit experiment, we can use the following formulas:

1. Slit Separation (d): d = λ * L / a

2. Width of Each Slit (w): w = λ * L / (n * a)

where: λ = wavelength of light (in meters) L = distance from the slits to the screen (in meters) a = distance between adjacent bright fringes (in meters) n = number of bright fringes (in this case, n = 7)

Given values: λ = 438 nm = 438 * 10^(-9) meters (convert from nanometers to meters) L = 2.35 m a = 1.05 mm = 1.05 * 10^(-3) meters (convert from millimeters to meters) n = 7

Let's start by calculating the slit separation (d):

1. Slit Separation (d): d = λ * L / a d = (438 * 10^(-9) meters) * (2.35 m) / (1.05 * 10^(-3) meters) d ≈ 0.0000098 meters d ≈ 9.8 * 10^(-6) meters

Next, let's calculate the width of each slit (w):

2. Width of Each Slit (w): w = λ * L / (n * a) w = (438 * 10^(-9) meters) * (2.35 m) / (7 * 1.05 * 10^(-3) meters) w ≈ 0.000014 meters w ≈ 14 * 10^(-6) meters

Finally, let's express the answers in micrometers (μm):

Slit Separation (d) ≈ 9.8 μm Width of Each Slit (w) ≈ 14 μm

So, the slit separation is approximately 9.8 micrometers, and the width of each slit is approximately 14 micrometers.