Question

Light from a laser strikes a diffraction grating that has 5500 lines per centimeter. The central and first-order maxima are separated by 0.455 m on a wall, 1.62 m from the grating, calculate the wavelength of the laser light.

Answer 1

.Answer:

491.4 nm

Explanation:

The distance between central and first maxima is,

$y=0.455m$

And the distance between screen abnd grating is,

$L=1.62 m$

Now the angle can be find as,

$tan\theta=\frac{y}{L} \\\theta=tan^{-1}(\frac{0.455}{1.62})  \\\theta=15.68^{\circ}$

Now the grating distance is,

$d=\frac{1}{5500} cm\\d=1.82\times 10^{-6}m$

Now with m=1 condition will become,

$\lambda=dsin\theta$

So,

$\lambda=1.82\times 10^{-6}m\times sin(15.68^{\circ})\\\lambda=1.82\times 10^{-6}m\times 0.270\\\lambda=491.4\times 10^{-9}m\\\lambda=491.4 nm$

Therefore the wavelength of laser light is 491.4 nm.