Question

White light strikes a diffraction grating which has $4,120$ slits per centimeter. A certain color of light creates a first order bright fringe at an angle of ${14.0}^{\circ }$ from straight ahead.
What is the wavelength of this light?

• A. $587nm$
• B. $985nm$
• C. $17,030nm$
• D. $170.3nm$
• E. $436nm$

Answer 1

The correct option is A $587nm$

Given : $\theta ={14}^o$ $⟹sin\left({14}^o\right)=0.242$

Number of slits per cm $=4120$

$\therefore$ Distance between each slit $d=\frac{0.01}{4120}=2.427\times {10}^{-6}$ $m$

Using $d$ $sin\theta =m\lambda$ where $m=1$ (first order)

$\therefore$ $2.427\times {10}^{-6}\times 0.242=1\times \lambda$ $⟹\lambda =0.587\times {10}^{-6}$ $m=587$ $nm$