Question

White light (light containing all frequencies of light in the visible spectrum) passes through a diffraction grating with 1300 lines per centimeter, and a screen is placed 2 meters away. What is the distance between the 1st order blue fringe and the 1st order red fringe? (for red light use red- 700 nm and for blue light use Ablue 450 nm).

Answer 1

The distance between the 1st order blue fringe and the 1st order red fringe is 6.5 cm.

Step-by-step explanation:

Given that,

Diffraction grating =1300 lines/cm

Distance of screen = 2 m

Order number = 1

We need to calculate the distance between the 1st order blue fringe and the 1st order red fringe

Using formula of distance

For first order red fringe

`d\sin\theta=m\lambda`

`d*(y)/(l)=m*\lambda`

`y_(r)=(m*\lambda l)/(d)`

`y_(r)=(1*700*10^(-9)*2)/((1)/(1300)*10^(-2))`

`y_(r)=0.182\ m`

For first order blue fringe

`y_(b)=(1*450*10^(-9)*2)/((1)/(1300)*10^(-2))`

`y_(b)=0.117\ m`

We need to calculate the distance between blue fringe and red fringe

`\Delta y=y_(r)-y_(b)`

`\Delta y=0.182-0.117`

`\Delta y=0.065\ m=6.5 cm`

Hence, The distance between the 1st order blue fringe and the 1st order red fringe is 6.5 cm.