Question

Experiment Setup: (How to experimentally determine the diffraction bright fringe angle). In your textbook problem, you were able to solve for the unknown laser wavelength because you were given the original diffraction grating spacing and the diffraction m=1 bright fringe angle. However, in lab, you will not be given the diffraction m=1 bright fringe angle because you are setting up the laser and the diffraction grating to measure the m=1 bright fringe angle. How will you measure this angle, because you will not have a protractor? Instead of directly measuring an angle, you will have to measure the lengths associated with the triangle that creates the angle, and to use trigonometry to calculate the angle from your length measurements. Going back to the setup outlined in Figure 1, describe what lengths you will measure in your experimental setup and how you will obtain the angle from those lengths.

Answer 1

In order to obtain the angle, you need to measure the lengths associated with the triangle that creates the angle, and to use trigonometry to calculate the angle from your length measurements. Here's how you can do it:

1. Set up the laser and diffraction grating as shown in Figure 1.

2. Place the screen at a distance L from the diffraction grating.

3. Turn on the laser and observe the diffraction pattern on the screen.

4. Locate the m=1 bright fringe, which is the first bright spot to the left or right of the central maximum.

5. Measure the distance from the center of the diffraction pattern to the m=1 bright fringe. Let's call this distance y.

6. Measure the distance from the diffraction grating to the screen. Let's call this distance L.

7. Measure the distance from the diffraction grating to the m=1 bright fringe. Let's call this distance d.

8. Now we can use trigonometry to calculate the angle θ between the central maximum and the m=1 bright fringe. The angle θ can be calculated using the equation: θ = tan^-1(y/L)

9. We can also use the diffraction grating equation to calculate the wavelength of the laser. The equation is given by: d sinθ = mλ, where d is the spacing between the diffraction grating lines, θ is the angle between the central maximum and the m=1 bright fringe, m is the order of the bright fringe, and λ is the wavelength of the laser.

Therefore, by measuring the lengths y, L, and d in the experimental setup, and using the trigonometry and diffraction grating equations, we can determine the diffraction bright fringe angle and the wavelength of the laser.

Step-by-step explanation:

Answer 2

In the experimental setup, we will measure the distance between the diffraction grating and the screen (L), as well as the distance between adjacent bright fringes on the screen (d). These two measurements will allow us to calculate the angle of the m=1 bright fringe using trigonometry.

To obtain the angle, we can use the small angle approximation, which states that for small angles, the tangent of the angle is approximately equal to the angle in radians. Thus, we can write:

tan θ ≈ θ

where θ is the angle of the m=1 bright fringe. From Figure 1, we can see that the distance between adjacent bright fringes on the screen (d) is related to the angle θ by:

d = λ/L * tan θ

where λ is the wavelength of the laser light, and L is the distance between the diffraction grating and the screen.

Solving for the angle θ, we get:

θ = arctan(d * L/λ)

Therefore, we can measure the distance between the diffraction grating and the screen (L) and the distance between adjacent bright fringes on the screen (d), and use the above equation to calculate the angle of the m=1 bright fringe. This allows us to experimentally determine the wavelength of the laser light, even without directly measuring the angle.