QUESTION If a diffraction grating has more lines per centimeter, how does that a

Question

QUESTION If a diffraction grating has more lines per centimeter, how does that affect the spacing of the lines on the grating and the separation between adjacent principal maxima?

The spacing of the lines on the grating remains the same.

The separation between adjacent maxima decreases.

The separation between adjacent maxima increases.

The spacing of the lines on the grating decreases.

The spacing of the lines on the grating increases.

Monochromatic light from a helium-neon laser ( = 632.8 nm) is incident normally on a diffraction grating containing 6.54 103 lines/cm. Find the angles at which one would observe the first-order maximum, the second-order maximum, and so forth.

a)

b)2

Suppose light with wavelength 7.80 102 nm is used instead and the diffraction grating has 3.60 103 lines per centimeter. Find the angles of all principal maxima. 0 = ° 1 = ° 2 = ° 3 = °

Explanation / Answer

a) spacing between lines is 1/grating lines/cm

since spacing is inversly protional to grating lines so grating lines increases,no of spacing decreases.

so answer is The spacing of the lines on the grating decreases.

b)lamda=632.8nm=632.8*10^-9 m

spacing=1/6.54810^3 lines /cm

=1.52*10^-6 m

using below formula

n*lambda = d*sin(theta)

for first order n=1

1*632.8*10^-9=1.52*10^-6 *sin theta

416.3*10^-3=sin theta

0.416=sin theta

theta=24.5 degree

for first order n=2

2*632.8*10^-9=1.52*10^-6 *sin theta

sin theta=0.832

theta=56.14 degrees

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