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

Answer:

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

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

$d\sin\theta=m\lambda$

$d\times\dfrac{y}{l}=m\times\lambda$

$y_{r}=\dfrac{m\times\lambda l}{d}$

$y_{r}=\dfrac{1\times700\times10^{-9}\times2}{\dfrac{1}{1300}\times10^{-2}}$

$y_{r}=0.182\ m$

For first order blue fringe

$y_{b}=\dfrac{1\times450\times10^{-9}\times2}{\dfrac{1}{1300}\times10^{-2}}$

$y_{b}=0.117\ m$

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.