High School

We appreciate your visit to Light from an argon laser strikes a diffraction grating that has 4223 lines per cm The central and first order principal maxima are separated by. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Light from an argon laser strikes a diffraction grating that has 4223 lines per cm. The central and first-order principal maxima are separated by 0.5 m on a wall 1.55 m from the grating. What is the wavelength of the laser light in nm?

Answer :

The wavelength of the laser light is approximately 76 nm.

We can use the equation for the position of the principal maxima:

d sinθ = mλ

where d is the distance between adjacent slits in the grating, θ is the angle between the incident light and the direction of the principal maximum, m is the order of the maximum, and λ is the wavelength of the light.

For the central maximum, m = 0, so we have:

d sinθ = 0

Since sinθ = 0 for θ = 0, this means that the central maximum is at θ = 0, or straight ahead.

For the first-order maximum, m = 1, so we have:

d sinθ = λ

We can solve for d by using the information about the separation of the central and first-order maxima on the wall:

y = L tanθ ≈ Lθ

where y is the distance between the central and first-order maxima on the wall, L is the distance from the grating to the wall, and we have used the small-angle approximation tanθ ≈ θ.

Thus, we have:

y = Lθ = L sin(θ) / cos(θ) = L sin(θ)

since cos(θ) is close to 1 for small angles.

Substituting d sinθ = λ, we get:

y = Lλ / d

We can solve for λ by plugging in the known values:

d = 1 / (4223 lines/cm * [tex]10^4[/tex] cm/m) = 2.365 *[tex]10^{-7[/tex] m

L = 1.55 m

y = 0.5 m

λ = y d / L = (0.5 m) (2.365 * [tex]10^{-7[/tex] m) / (1.55 m) ≈ 7.6 * [tex]10^{-8[/tex] m = 76 nm

Therefore, the wavelength of the laser light is approximately 76 nm.

To learn more about wavelength visit:

https://brainly.com/question/31143857

#SPJ11

Thanks for taking the time to read Light from an argon laser strikes a diffraction grating that has 4223 lines per cm The central and first order principal maxima are separated by. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada