White light is spread out into its spectral components by a diffraction grating. If the grating has 2000 lines per centimeter, at what angle does red light of wavelength 640 nm …

Question

asked Jul 4, 2020 35.5k views

2 Answers

Roberto Leinardi · Answer 1 · 2020-07-04T09:53:58+0000

Answer:
$7.35\°$

Step-by-step explanation:

The diffraction angles
$\theta_(n)$ when we have a slit divided into
parts are obtained by the following equation:

$dsin\theta_(n)=n\lambda$ (1)

Where:

is the width of the slit

$\lambda$ is the wavelength of the light

is an integer different from zero

Now, the first-order diffraction angle is given when
n=1 , hence equation (1) becomes:

$\theta_(1)=arcsin((\lambda)/(d))$ (2)

We are told the diffraction grating has 2000lines per cm, this means:

d=(1cm)/(2000)=0.0005cm=0.000005m

In addition we know
$\lambda=640nm=640(10)^(-9)m$

Solving (2) with the known values we will find
$\theta$ :

$\theta_(1)=arcsin(\frac640(10)^(-9) m}{0.000005m})$ (3)

$\theta_(1)=7.35\°$ (4) This is the angle at which red light appears in first-order spectrum.

Hemant Bavle · Answer 2 · 2020-07-10T13:37:07+0000

Step-by-step explanation:

It is given that,

If the grating has 2000 lines per centimeter.

Wavelength,
$\lambda=640\ nm=640* 10^(-9)\ m$

The principal maxima is given by :

$d\ sin\theta=n\lambda$

Since, d = 1/N and n = 1

So,
$d=(1)/(2000\ lines/cm)=0.0005\ cm$

$d=5* 10^(-6)\ m$

$sin\theta=(\lambda)/(d)$

$sin\theta=(640* 10^(-9))/(5* 10^(-6))$

$\theta=7.35^(\circ)$

So, the angle is 7.35 degrees. Hence, this is the required solution.