Name: Diffraction Grating
Uploaded: 2019-07-19
Duration: 5 min 57 s
Description: A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions.

Question

White light is incident normally on a diffraction grating with a slit-separation $d$ of $2.00 \times 10^{- 6} m$ . The visible spectrum has wavelengths between $400 nm$ and $700 nm$ .

(a) Calculate the angle between the red and violet ends of the first-order spectrum.

Accepted Answer

We know that the equation for a diffraction grating is

$d \sin θ = nλ$

where $d$ Is the distance between adjacent lines of the grating $θ$ Is the angle between the zeroth order and $n^{th}$
Order maximum, and $λ$ Is the wavelength of the light incident normally at the grating.

For red light, rearrange $d \sin θ = nλ$ or $\sin θ = \frac{nλ}{d}$

Given, $d = 2.00 \times 10^{- 6} m$ , $n = 1$ , $λ = 700 nm = 700 \times 10^{- 9}$

$∴ {sinθ}_{Red} = \frac{1 \times 700 \times 10^{- 9}}{2.00 \times 10^{- 6}} = 0.350,$

$∴ θ_{red} = 20.5 °$

Again, For violet light, rearrange $d \sin θ = nλ$ or $\sin θ = \frac{nλ}{d}$

Given, $d = 2.00 \times 10^{- 6} m$ , $n = 1$ , $λ = 400 nm = 400 \times 10^{- 9}$

$∴ {sinθ}_{violet} = \frac{1 \times 400 \times 10^{- 9}}{2.00 \times 10^{- 6}} = 0.200,$

$∴ θ_{violet} = 11.5 °$

Therefore, angular separation
$= 20.5 ° - 11.5 ° = 9.0 ° .$

David Sang and Graham Jones Solutions for Chapter: Superposition of Waves, Exercise 11: Question

David Sang Physics Solutions for Exercise - David Sang and Graham Jones Solutions for Chapter: Superposition of Waves, Exercise 11: Question

Questions from David Sang and Graham Jones Solutions for Chapter: Superposition of Waves, Exercise 11: Question with Hints & Solutions

Learn and Prepare for any exam you want !