Diffraction grating #1 has half the lines/cm that diffraction grating #2 does. When used with a certain wavelength of light, both gratings give first order maxima. Which of the following statements is true for the same wavelength of light.
Grating #2 must give a second order maximum.
Both gratings must also give second order maxima.
It is possible that neither grating gives a second order maximum.
Grating #1 must give a second order maximum.
Grating #1, which has less dispersion, will have a second order maximum where grating # 2 has its first order maximum.
Choose the last answer.
The correct statement for the same wavelength of light is:
The angle of diffraction produced by diffraction grating #1 is twice the angle of diffraction produced by diffraction grating #2.
This is because the angle of diffraction is inversely proportional to the number of lines per unit length on the grating. Since diffraction grating #1 has half the lines/cm compared to diffraction grating #2, it will produce an angle of diffraction that is twice as large.
To find the correct statement, let's first consider the formula for the diffraction grating:
dsinθ = mλ
where d is the spacing between the lines of the grating, θ is the angle of the diffraction pattern, m is the order of the maximum, and λ is the wavelength of the light.
Since diffraction grating #1 has half the lines/cm that diffraction grating #2 does, we can conclude that the spacing between the lines of grating #1 (d1) is twice the spacing of grating #2 (d2).
Now, let's consider the first-order maximum, which corresponds to m = 1 in the equation. For this case, the equation becomes:
dsinθ = λ
Since we are using the same wavelength of light for both gratings, we can rewrite the equation as:
d1sinθ1 = d2sinθ2
Since d1 = 2d2 (given), the equation becomes:
2d2sinθ1 = d2sinθ2
Dividing both sides by d2:
2sinθ1 = sinθ2
From this equation, we can conclude that the angle of diffraction (θ) for grating #1 (θ1) is twice the angle of diffraction for grating #2 (θ2). Therefore, the correct statement is:
"The angle of diffraction for the first-order maximum is twice as large for diffraction grating #1 compared to diffraction grating #2."