1. How many lines per centimeter does a grating have if the third-order occurs a

Question

1. How many lines per centimeter does a grating have if the third-order occurs at a 17.6° angle for 630 nm light?

3. Two first-order spectrum lines are measured by an 9550 line/cm spectroscope at angles, on each side of center, of +25°35', +41°03' and -25°45', -41°15'. What are the wavelengths? lower angles? higher angles?

4. Two Polaroids are aligned so that the light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently reduced by 40 percent?

5. Unpolarized light passes through four successive Polaroid sheets, each of whose axis makes a 44° angle with the previous one. What is the intensity of the transmitted beam?

PLEASE HELP ME. I'M RUNNING LOW ON THE QUESTIONS REMAINING IN MY SUBSCRIPTION PERIOD. please show complete answer. THANK YOU SO SO MUCH.

Explanation / Answer

4.

After passing through polaroid intensity is given by:

I1 = I0*(cos A)^2

A = arccos (sqrt (I1/I0))

Given that intensity is reduced by 40 %, so I1/I0 = 0.60

So angle should be:

A = arccos (sqrt 0.6) = 39.23 deg

5.

Initial intensity = I0

because light is initially unpolarised, after going through first polariser intensity will halved.

After the first polariser

I = I0/2

After that intensity is reduced by (cos^2 A) factor

after second polarizer intensity will be = (I0/2)*(cos^2 A)

after 3rd polarizer intensity will be = (I0/2)*(cos^4 A)

after 4th polarizer intensity will be = (I0/2)*(cos^6 A)

A = 44 deg

So,

If = (I0/2)*(cos 44 deg)^6 = 0.0692*I0

If = 6.92% of initial intensity

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