Find the angle between the first minima for the two sodium vapor lines, which ha

Question

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 1.40 mu m. What is the distance between these minima if the diffraction pattern falls on a flat screen 1.40 m from the slit? mm Discuss the ease or difficulty of measuring such a distance. (Select all that apply.) This distance is easily measured using a magnifying glass. This distance is easily measured using a microscope. This distance is easily measured by the human eye.

Explanation / Answer

Part A)

Apply sin(angle) = m(wavelength)/a

For the first wavelength

sin(angle) = (1)(589.1 X 10^-9)/(1.4 X 10^-6)

angle = 24.88420286 degrees

For the second wavelength

sin(angle) = (1)(589.6 X 10^-9)/(1.4 X 10^-6)

angle = 24.90676188 degrees

The difference is 24.90676188 - 24.88420286 = 0.0226 degrees

Part B)

y = m(wavelength)L/a

y - y = mL(wavelength - wavelength)/a

y - y = (1)(1.4)(589.6 X 10^-9 - 589.1 X 10^-9)/(1.4 X 10^-6)

y-y = 5 X 10^-4 m which is 0.5 mm

Part C

A magnifying glass may be able to measure that. A microscope would definitely be able to help. With a half a mm, the human eye would have trouble with that measurement being accurate.

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