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

Step-by-step 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=(y)/(L) \\\theta=tan^(-1)((0.455)/(1.62))  \\\theta=15.68^(\circ)`

Now the grating distance is,

`d=(1)/(5500) cm\\d=1.82* 10^(-6)m`

Now with m=1 condition will become,

`\lambda=dsin\theta`

So,

`\lambda=1.82* 10^(-6)m* sin(15.68^(\circ))\\\lambda=1.82* 10^(-6)m* 0.270\\\lambda=491.4* 10^(-9)m\\\lambda=491.4 nm`

Therefore the wavelength of laser light is 491.4 nm.