(a) Find the angle between the first minima for the two sodium vapor lines, whic

Question

(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.80 µm.


(b) What is the distance between these minima if the diffraction pattern falls on a flat screen 1.50 m from the slit?
mm

(c) Discuss the ease or difficulty of measuring such a distance. (Select all that apply.)

a)This distance is easily measured using a magnifying glass.

b)This distance is easily measured by the human eye.

c)This distance is easily measured using a microscope.

Explanation / Answer

D sin(theta) = m
Where m is order of minima .
theta = is the angle relative to the original direction of the light
D is the width of slit = 2.8 * 10^-6m

For = 589.1 * 10^-9 m and m= 1 (first minima)
2.8 * 10^-6 * sin(theta) = 1 * 589.1 * 10^-9
sin (theta) = 0.21039
theta = sin^-1 (0.21039)
theta = 12.1450

For = 589.6 * 10^-9 m and m= 1 (first minima)
2.8 * 10^-6 * sin(theta) = 1 * 589.6 * 10^-9
sin (theta) = 0.21057
theta = sin^-1 (0.21057)
theta = 12.1550

Difference = 12.155 - 12.145 = 0.0100

b)
Let y be the distance from the center of the central diffraction maximum to the first diffraction minimum
L = Distance of screen from slit = 1.5 m
y1 = L / a
y1 = 1.5 * 589.1 * 10^-9 m / 2.8 * 10^-6
y1 = 0.3155m

y1 = L / a
y1 = 1.5 * 589.6 * 10^-9 m / 2.8 * 10^-6
y1 = 0.3158m

Distance between minima = 0.0003 m = 0.03cm

c) This distance is easily measured using a magnifying glass.

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