Question

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.78 m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 2.66 mm . What is the difference between these wavelengths? Express your answer in meters.

Answer 1

Answer:
`0.62* 10^(-8)=10.62 nm`

Step-by-step explanation:

Given

No of lines in the grating (N)=900 slits per centimeter

Distance between screen and grating(L)=2.78 m

Slit width(d) =
`(1)/(N)=1.11* 10^(-5)m`

We know distance between two maxima

`\dealta y=\left ( (\lambda _1-\lambda _2)/(d)\right )L`

therefore

`\lambda _1-\lambda _2=(d\delta y)/(L)`

`\lambda _1-\lambda _2=(1.11* 10^(-5)* 2.66* 10^(-3))/(2.78)`

`\lambda _1-\lambda _2=10.62* 10^(-8)=10.62 nm`