Question

I need help with these question. please show step by step solution. make sure the answer is correct.

Question 1 (1 point) In a double-slit experiment it is found that light of a wavelength 512 nm gives a second-order maximum at a certain location on the screen. What wavelength of light would have a minimum at the same location? Your Answer: Answer units Question 2 (1 point) A thin oil slick (n=2.0) floats on water (n=1.33). A beam of white light strikes the oil at normal incidence from air. The only enhanced reflected wavelengths are 240 nm and 400 nm. What is the minimum thickness of the oil slick? Your Answer: Answer units

Answer 1

1)

for maximum,

dsin$\theta$ = m$\lambda$

second order means m = 2 ,

dsin$\theta$ = 2 * 512 = 1024 nm

so,

for minimum

(m+1/2)$\lambda$ = 1024

for m = 0 , $\lambda$ = 2048 nm

for m = 1, $\lambda$ = 683 nm

for m = 2, $\lambda$ = 410 nm

visible range is 380 to 700 nm

so,

both 410 nm and 683 nm are correct !!!

(The question should have told something about visible range, but as there was no information, I gave two wavelengths, both are right !)

____________________________________________

2)

2t = ( m₁ + 1/2)400

  2t = ( m₂ + 1/2)240

2m₁ + 1 = 400 --------- (1)

2m₂ + 1 = 240 ---------- (2)

divide both equations, we have

2m1 + 1 / 2m2 + 1 = 5/3

so,

2m1 + 1 = 5 gives

m1 = 2

and

2m2 + 1 = 3 gives

m2 = 1

so,

we can either use (1) or (2)

2t = ( 1 + 1/2) 400/2

t = 150 nm