A beam of light contains all wavelengths between 500 nm and 640 nm and is incide
ID: 1696397 • Letter: A
Question
A beam of light contains all wavelengths between 500 nm and 640 nm and is incident on a diffraction grating with 150 lines/mm
If two consecutive orders are overlapping, what can you say about the angles of the high and low wavelength light from the two orders?
A. [500nm] higher order > [640nm] lower order
B. [500nm] higher order < [640nm] lower order
C. [640nm] higher order < [500nm] lower order
D. [640nm] higher order = [500nm] lower order
What is the lowest order that is overlapped by anothe
order?
m=__________
What is the highest order for which the complete wavelength range of the beam is present?
m=__________
What is the greatest angle at which the light with the shortest wavelength appears?
_________degrees
-Thank you
Explanation / Answer
wavelength of the light beams is _1 = 500 *10^-9 m
_2 = 640 *10^-9 m
a ) m_1 / m_2 = _2 / _1
= 640 *10^-9 m / 500*10^-9 m
= 1.28
13/10
m_1 = 13 , m_2 = 10
b ) m_1 _1 = d sin _1
_1 = sin ' ( m_1 _1 / d )
= sin ' ( 13 * 500 *10^-9 m / 6.66*10^- 6 m ) ( d = 1/ N
= 1/ 150 lines / mm
= 6.66 *10^-6 m )
= 77.4 degrees
c )
m_2 _2 = d sin _2
_2 = sin ' ( m_2 _2 / d )
= sin ' ( 10 * 640 *10^-9 m / 6.66*10^- 6 m )
= 73.9 degrees
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