Question

Suppose that you have a reflection diffraction grating with
*n*= 105 lines per millimeter. Light from a sodium lamp
passes through the grating and is diffracted onto a distant
screen.

Two visible lines in the sodium spectrum have wavelengths 498
nmand 569 nm. What is the angular separation ?*?* of the
first maxima of these spectral lines generated by this diffraction
grating?

How wide does this grating need to be to allow you to resolve
the two lines 589.00 and 589.59 nanometers, which are a well known
pair of lines for sodium, in the second order (*m*=2)?

Answer #1

dsin = m

a) n= 105 lines per mm = 105000 lines per m

( 1/ 105000 ) sin = 1 (498 x 10^-9)

1 = sin^-1( 105 x 498 x 10^-6) = 2.997363 degree apprx

( 1/ 105000 ) sin 2= 1 (569 x 10^-9)

2= 3.425176

delta = 0.427813 degree apprx

b)

Chromatic Resolving power,

R = ? / ??= m ( width)( number of lines on grating)

589/ 0.59 = 2(width)( 105)

width = 4.7538 mm apprx

A diffraction grating is made with 750 lines per millimeter is
illuminated with violet light of wave length 400nm. How many lines
can be observed with this grating? If the intense white light is
incident on the same diffracting grating what is the angular
separation between the violet edge (400nm) and red edge (700nm)?
What is the highest order in which the complete visible spectrum
can be seen using this grating (λ =400-700nm)?

A grating has 810 lines per centimetre, and a flat screen is
perpendicular to the ray that makes the central peak of the
diffraction pattern. The screen is 2.20 m from the grating. If
light of two wavelengths, 630 nm and 670 nm, passes through the
grating, what is the separation on the screen between the
fourth-order maxima for the two wavelengths?

Light from a Hydrogen lamp is focused through a diffraction
grating with 770 lines/cm and the diffraction pattern is shown on a
screen that is 5.30 m away. You notice in the pattern that there
are two distinct purple dots that are 16.46 cm and 17.70 cm from
the central maximum, corresponding to the first-order maxima for
two different wavelengths of light emitted by the lamp. What is the
difference between the two wavelengths (in nm)
corresponding to these purple...

Light of wavelength 600 nm shines on a diffraction grating that
has 400 lines per cm. The light emerging from the grating hits a
screen 50 cm wide so that the central maximum is exactly in the
middle of the screen. Assume that the screen is 3 m from the
grating.
How many maxima appear on the screen?
(a)
4
(b)
6
(c)
7
(d)
5
(e)
3

You have a diffraction grating with 3000 lines/cm. You also have
a light source that emits light at 2 different wavelengths, 428 nm
and 707 nm, at the same time. The screen for your experiment is 1.5
meters from the diffraction grating.
A. What is the line spacing for the grating?
B. What is the difference in the angle of the 2nd bright fringe
for each wavelength for this grating?
C. Which wavelength is closer to the center of the...

A light source is directed into a 100x100 mm diffraction grating
at an agle of 20 degrees relative to the grating's normal. The
grating has a ruling density of 1200 lines/mm. A 100 cm long screen
is placed 50 cm from the grating and the dispersed spectrum is
displayed on the screen. The screen is placed so it is directly in
front of the grating. You observe the visible spectrum that runs
from 400 nm to 800 nm.
Calculate the...

1. A diffraction grating is used to separate the spectral lines
of light, emanating from a gas discharge tube (e.g., a neon light),
that is normally incident on the grating. On a screen placed 2.0 m
from the grating, the third-order (m = 3) interference maximum for
violet light (λ = 4.4 × 10−7 m) is found to be 0.20 cm farther from
the location of the central maximum (m = 0) on the screen than the
second-order maximum of...

1. Intense white light is incident on a diffraction grating that
has 752 lines/mm.
(a) What is the highest order in which the complete visible
spectrum can be seen with this grating? (Enter 1 for first order, 2
for second order, etc.)
(b) What is the angular separation between the violet edge (400 nm)
and the red edge (700 nm) of the first order spectrum produced by
the grating?
2. The angle of incidence of a light beam in air...

Astronomers use diffraction gratings to study the spectra of
light from stars. For stars like the Sun, Calcium produces a pair
of spectral features called the H and K lines at wavelengths of
396.9 nm and 393.4 nm, respectively. One of the spectrographs on
the Keck telescope contains a diffraction grating with 1200
lines/mm. What is the angular separation between the H and K lines
in the second order produced by this spectrograph?
Astronomers use diffraction gratings to study the...

The spectrum of light from heated up hydrogen gas has only a few
wavelengths present. These are known as spectral lines. It includes
a red line at 656 nm and a blue-violet line at 434 nm. What are the
angular separations between these two spectral lines for all
visible orders obtained with a diffraction grating that has 4770
grooves/cm? (In this problem assume that the light is incident
normally on the grating.)
I'm having trouble with this question as I'm...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 20 minutes ago

asked 42 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago