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:$0.62\times 10^{-8}=10.62 nm$

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) =$\frac{1}{N}=1.11\times 10^{-5}m$

We know distance between two maxima

$\dealta y=\left ( \frac{\lambda _1-\lambda _2}{d}\right )L$

therefore

$\lambda _1-\lambda _2=\frac{d\delta y}{L}$

$\lambda _1-\lambda _2=\frac{1.11\times 10^{-5}\times 2.66\times 10^{-3}}{2.78}$

$\lambda _1-\lambda _2=10.62\times 10^{-8}=10.62 nm$