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As in the diagram on p.04.9, a white light beam passes through a diffraction gra

ID: 2252393 • Letter: A

Question

As in the diagram on p.04.9, a white light beam passes through a diffraction grating with a slit spacing of d = 0.010 mm and several rainbow spectra are projected onto a screen a distance L = 1.500 m away. How far from the center of the screen (the theta = 0 position) is the red end of the n=2 spectrum? How far from the center is the violet end of the n=2 spectrum? The wavelength of red light is approximately 700 nm; the wavelength of violet light is 400 nm. Make a qualitative sketch showing what the graph of L/x vs. a/X should look like in part 1. What is the slope of this plot? (Make L large in order to be able to measure the distances with high precision.)

Explanation / Answer

1. Given lambda red = 700 nm, n = 2

condition n lambda = d sin(theta)

sin (theta) = (2x 700x10^-9)/0.01x10^-3

= 0.14 m

theta = sin^-1(0.14) = 8.048 degree

Tan(8.048)=y(red)/1500

y(red) = 0.1414x1500 = 212.08 mts


Given lambda violet = 400 nm, n = 2

condition n lambda = d sin(theta)

sin (theta) = (2x 400x10^-9)/0.01x10^-3

= 0.08 m

theta = sin^-1(0.08) = 4.588 degree

Tan(4.588)=y(violet)/1500

y(red) = 0.1414x1500 = 120.37 mts


2) Actually both are same L/x = a/lambda, So the slop is a straight line passes through origin having solpe 45