I have this problem in physics. I need help finding the calculated frequency of

Question

I have this problem in physics. I need help finding the calculated frequency of a laser.

They gave two formulas to solve for this:

Theta=tan-1 (x/D)

x in the formula is 0.04 meters

D in the formula can be either 1.63 meters or 0.233 meters. But i'm pretty sure it's 1.63 meters.

Theta is the angle of diffraction. I can't seem to solve it properly.

Then, d (sin theta)=n lamda

In this formula,

d is the distance between the slits of a CD. d is 1.6 micrometers.

theta is the angle of diffraction found using the first formula

n is the order of spots. The n=1 order is 0.04 meters and the n=2 order is 0.08 meters.

And finally, lamda is the wavelength. This is an unknown value. The second formula find this.

There's just one problem, in my project it says calculate the frequency using that formula. But they also say compare it to the actual wavelength of the laser. Which on the back of the packaging, it says 650 nm plus or minus 10 nm.

Thank you so much for your help!

Be sure to show all of your calculations please!

Explanation / Answer

First of all we will find the value of the theta -

theta = tan^-1 (x / D)

Put the values as given -

theta = tan^-1 (0.04 / 1.63) = tan^-1 (0.0245) = 1.405 deg.

Now take the another expression to find the value of lemda -

d (sin theta) = n * lemda

take, n = 1, and d = 1.6 micrometer = 1.6 x 10^-6 m and n = 1 order is 0.04 m

put the values -

(1.6x10^-6)x(sin1.405) = 0.04 * lemda

=> lemda = 0.97975 x 10^-6 = 979.75 x 10^-9 m = 979.75 nm

like-wise -

when we use, n=2 order is 0.08 m

lemda = 490.39 nm.

Now come to the point.

You have mentioned that the actual wavelength of the laser is 650 nm.

There is a far difference between the calculated and theoretical value.

So, please check the results and in case of any doubt, donot hiesitate to ask.

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