Question

A diffraction grating produces a second maximum that is 89.7 cm from the central maximum on a screen 2.0 m away. If the grating has 6000 lines per centimeter, what is the wavelength of the light that produces the diffraction pattern?

Answer 1

The wavelength of the light that produces the diffraction pattern is 2691 nm.

Step-by-step explanation:

To determine the wavelength of the light that produces the diffraction pattern, we can use the formula:

Ay = xλ/d

Where Ay is the distance between adjacent fringes, x is the distance from the central maximum to the second maximum (89.7 cm), d is the slit separation equal to the number of lines per centimeter (6000 lines/cm), and λ is the wavelength of light we want to find.

Plugging in the given values, we can solve for λ:

89.7 cm = xλ/(6000 lines/cm)

λ = (89.7 cm x 6000 lines/cm) / x

Since x is 2.0 m away, we need to convert it to cm:

x = 2.0 m x 100 cm/m = 200 cm

Substituting the values, we find:

λ = (89.7 cm x 6000 lines/cm) / 200 cm = 2691 nm

Therefore, the wavelength of the light that produces the diffraction pattern is 2691 nm.