1) Suppose that we have a pair of slits that have a very narrow 2.0 m separation
ID: 1342986 • Letter: 1
Question
1) Suppose that we have a pair of slits that have a very narrow 2.0 m separation. If a 650 nm red laser is passed through the slits, calculate the angle where the 1st, 2nd, and 3rd order spots will be found. Where is the 4th order spot? Explain.
2) White light passes through a pair of slits that are 0.170 mm apart and are 0.050 mm wide. The transmitted light falls on a screen 3.50 m away from the slits. It is found that the colors are separated on each of the spots. How big is the rainbow observed on the 1st order spot? In other words, what is the distance between the 750 nm red line and the 380 violet line as measured on the screen?
Explanation / Answer
from the diffraction formula
d sin theta = mL
for 1 st order
theta 1 = sin^-1 (mL/ d)
= sin^-1 ( 1 ( 650 * 10 ^-9 m/ 2* 10 ^-6 m)
= 18.96
for 2st order
theta 2 = sin^-1 (mL/ d)
= sin^-1 ( 2 ( 650 * 10 ^-9 m/ 2* 10 ^-6 m)
= 40.54
theta 3= sin^-1 (mL/ d)
= sin^-1 ( 3 ( 650 * 10 ^-9 m/ 2* 10 ^-6 m)
= 77.16
theta 4= sin^-1 (mL/ d)
= sin^-1 ( 4 ( 650 * 10 ^-9 m/ 2* 10 ^-6 m)
= infinity
so 4 th order spot cannot found
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