Distance between dark fringes in double slit demo with fluid

[science.girl]

Homework Statement

In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 x 10^-6 m, and the distance d between the centers of the slits is 1.8x10^-5 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits. Your notebook shows the following setup for the demonstration.

See page 11: http://apcentral.collegeboard.com/apc/public/repository/ap09_frq_physics_b.pdf

(a) Calculate the frequency of the light.

(b) Calculate the distance between two adjacent dark fringes on the screen.

The entire apparatus is now immersed in a transparent fluid having index of refraction 1.4.
(c) What is the frequency of the light in the transparent fluid?

(d) Does the distance between the dark fringes increase, decrease, or remain the same?

_____ Increase _____ Decrease _____ Remain the same

Explain your reasoning.

Homework Equations

f = c/$$\lambda$$

y_dark = [$$\lambda$$L/d][m+.5]

The Attempt at a Solution

A) f = c/$$\lambda$$
f = (3.0*10^8 m/s)/(5.5*10^(-7) m) = 165Hz

B) y_dark = [$$\lambda$$L/d][m+.5]
Hmm... would you have to find a $$\Delta$$y, though? How would you do this?

 

[rl.bhat]

Find y_{m and ym+1 for dark fringes and find the difference.
What is the relation between the refractive index of the material and wavelength of light traveling through?}

 

[Andrew Mason]

Homework Equations

f = c/$$\lambda$$

y_dark = [$$\lambda$$L/d][m+.5]

The Attempt at a Solution

A) f = c/$$\lambda$$
f = (3.0*10^8 m/s)/(5.5*10^(-7) m) = 165Hz

Careful with handling exponents: 8 - (-7) = ? You can tell that this number is way off.

B) y_dark = [$$\lambda$$L/d][m+.5]
Hmm... would you have to find a $$\Delta$$y, though? How would you do this?

How would you find the y position of successive dark lines? (Hint: what is m?) How would you find the difference in the y position of these dark lines?

AM

 

[science.girl]

Careful with handling exponents: 8 - (-7) = ? You can tell that this number is way off.

How would you find the y position of successive dark lines? (Hint: what is m?) How would you find the difference in the y position of these dark lines?

AM

Oops! (A) should be 5.45*10^14 Hz.

For (B):
rl.bhat says to "Find y_m and ym+1 for dark fringes and find the difference."
Hmm... I'm going to think about this one some more. Any hints, maybe?
I'll keep you updated.

 

[Redbelly98]

For (B):
rl.bhat says to "Find y_m and ym+1 for dark fringes and find the difference."
Hmm... I'm going to think about this one some more. Any hints, maybe?

Use the equation you wrote earlier:

y_dark = [λL/d][m+.5]

Evaluate the RHS for m and also for m+1. Subtract the two expressions and see what you get.

 

[science.girl]

Use the equation you wrote earlier:


Evaluate the RHS for m and also for m+1. Subtract the two expressions and see what you get.

Oh! I understand now! Thank you very much.

For (c), I used the v = c/n, and used the velocity in the equation v = f$$\lambda$$ to determine the frequency. Is this correct?

For (d), under what conditions would the dark fringes move closer or farther away? What should I be analyzing?

 

[Redbelly98]

(c) Correct

(d) Two things to think about here:

1. What happens to the wavelength when the medium is changed from n=1 to n=1.4?
2. How does the fringe spacing change when wavelength is either increased or decreased?

 

[science.girl]

Perfect! Thank you.