Working on your car you spill oil (index of refraction = 1.55) on the ground int

Question

Working on your car you spill oil (index of refraction = 1.55) on the ground into a puddle of water (n = 1.33). You notice a rainbow pattern appear across the oil slick. Recalling the lessons you learned in physics class, you realize you can calculate where constructive and destructive interference occurs based on the thickness of the oil slick. (Assume that the average wavelength is 558 nm.)

(a) What are the first three thicknesses necessary for constructive interference?
nm
nm
nm

(b) What are the first three thicknesses necessary for destructive interference?
nm
nm
nm

Explanation / Answer

The condition for constructive interference is

2tn=(m+1/2)?

the minimum thickness is observed at m=0

t=?/4n

=558 nm/4(1.55)

=90 nm

for m = 1

2tn=(1+1/2)?

t=3?/4n

= 3 (558nm)/4(1.55)

=270 nm

for m =2

2tn=(2+1/2)?

t=5?/4n

= 5(558 nm)/4(1.55)

=450nm

----------------------------------------------------------------

the condition for distructive inter fere ce is

The condition for constructive interference is

2tn=(m)?

for m = 0

t = 0

the minimum thickness is observed at m=1

t = ?/ 2n = 558 nm/ 2 ( 1.55 ) = 180 nm

for m = 2

the minimum thickness is observed at m=2

t = 2?/ 2n = 2 (558 nm)/ 2 ( 1.55 ) = 360 nm

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.