Question

A screen is placed 1.25 m away from a diffraction grating. The grating has 4600.0 lines per centimeter and is illuminated with light of wavelength 599 nm. Calculate the distance between the first-order and second-order fringes on the screen.

Answer 1

The distance between the first-order and second-order fringes on the screen is 2.76 cm and 5.52 cm respectively.

Step-by-step explanation:

To calculate the distance between the first-order and second-order fringes on the screen, we can use the formula: Ay = xλ/d, where Ay is the distance between adjacent fringes, x is the order of the fringe (1 for first-order, 2 for second-order), λ is the wavelength of light, and d is the line separation of the diffraction grating.

In this case, the diffraction grating has 4600.0 lines per centimeter, which corresponds to a line separation of 0.000217 cm. The wavelength of the light is 599 nm, or 0.000599 cm. Plugging in these values into the formula, we get Ay = (x)(0.000599 cm) / (0.000217 cm).

For the first-order fringe (x = 1), Ay = (1)(0.000599 cm) / (0.000217 cm) = 2.76 cm. For the second-order fringe (x = 2), Ay = (2)(0.000599 cm) / (0.000217 cm) = 5.52 cm.