Question

The figure (Intro 1 figure) shows the interference pattern obtained in a double-slit experiment with light of wavelength λ.

Part A

Identify the fringe or fringes that result from the interference of two waves whose phases differ by exactly 2λ.

Enter the letter(s) indicating the fringe(s) in alphabetical order. For example, if you think that fringes A and C are both correct, enter AC.

Part B

The same double-slit experiment is then immersed in water (with an index of refraction of 1.33) and repeated. When in the water, what happens to the interference fringes?

They are more closely spaced than in air by a factor of 1.33.   They are more widely spaced than in air by a factor of 1.33.   They are spaced the same as in air.   They are shifted upward.   They are shifted downward.

Answer 1

Here the waves differ by a path difference byΔx=2λ

We have phase differenceΔφ=2π/λ*Δx

Δφ=4π

we have condition for constructive interference asΔφ=2nπ

where n is an integer

n=0 for central bright fringe

n=+/-1 for first maximas on both sides

n=+/-2 for the second maximas on boths sides

so Δφ=4π refers to A and D bright fringes

If the whole apparatus is immersed in water then the fringewidth decreases by an amount μ

where μ is the refractive index of water.

Hence the right answer is

They are more closelyspaced than in air by a factor of 1.33.