Question

24.73 . LIght is incident on a diffraction grating with 8600 lines/cm , and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists of two wavelengths, 4.5×10?7 m and 6.9×10?7 m .

Part A Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.

Answer #1

given

1 / ( a + b ) = 8600 lines/cm

or

1 / ( a + b ) = 860000 lines/m

( a + b ) sin = n

for first order bright fringes n = 1

then sin = / ( a + b )

= sin^{-1} (
/ ( a + b ) )

then now,

_{1}
= sin^{-1} (
/ ( a + b ) )

= sin^{-1} ( 6.9 X 10^{-7} X 860000)

_{1}
= 36.4^{o}

same way

_{2}
= sin^{-1} (
/ ( a + b ) )

= sin^{-1} ( 4.5 X 10^{-7} X 860000)

_{2}
= 22.77^{o}

now

Y_{n} = D tan_{1}

= 2.5 X tan36.4

= 1.843 m

sameway

Y_{n} ' = D tan_{2}

= 2.5 X tan22.77

= 1.05m

the linear distance between the first-order bright fringes of these two wavelengths on the screen is

Y = Y_{n} - Y_{n} '

Y = 1.843 - 1.05

Y = 0.793 m

**so the linear distance between the first-order bright
fringes of these**

**two wavelengths on the screen is Y = 0.793
m**

A diffraction grating with 600 lines/mm is illuminated with
light of wavelength 510 nm. A very wide viewing screen is 2.6 m
behind the grating.
What is the distance between the two m = 1 bright fringes?
How many bright fringes can be seen on the screen?

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...

Monochromatic light of wavelength 588 nm is incident upon a
diffraction grating that contains 8500 lines spread out over a
distance of 1.5 cm.
a) What is the line spacing of the grating?
b) At what angle does the 2nd principle maximum occur?
c) If the screen is located a distance of 1.55 m from the
grating, what is the linear distance on
the screen that separates the central maximum with the 2nd order
principle maximum?

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
student shines a monochratic light through a diffraction grating
with 4,000 lines per cm. the distance between the grating and the
screen is 1.2 m. The student measures the distance between the
first order fringe and central maxima at 0.2cm. What is the
frequency of the monochromatic light? Show work.

A 550 lines/mm diffraction grating is illuminated by light of
wavelength 520 nm.
How many bright fringes are seen on a 3.7-m-wide screen located
2.1 m behind the grating?

Sunlight is incident on a diffraction grating that has 3,550
lines/cm. The second-order spectrum over the visible range (400-700
nm) is to be limited to 2.05 cm along a screen that is a distance
L from the grating. What is the required value of
L?

Light from a hydrogen source is incident on a diffraction
grating. The incident light contains four wavelengths: λl = 410.1
nm, λ2 = 434.0 nm, λ3 = 486.1 nm, and λ4 = 656.3 nm. The
diffraction grating has 410 lines/mm. Calculate the angles between:
λl and λ4 in the first-order spectrum λl and λ3 in the third-order
spectrum

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...

White light is incident upon a diffraction grating with 1200
lines per mm. What is the angle between the red light (700 nm) and
green light (550 nm) leaving the grating in the first order bright
fringe?
a.
32.8 degrees
b.
24.5 degrees
c.
57.2 degrees
d.
15.9 degrees

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 10 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 33 minutes ago

asked 58 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago