# Homework Help: Light Question

1. Jun 5, 2009

### science.girl

1. The problem statement, all variables and given/known data
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

2. Relevant equations
f = c/$$\lambda$$

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

3. The attempt at a solution

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

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

Last edited by a moderator: Apr 24, 2017
2. Jun 6, 2009

### rl.bhat

Find ym 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?

3. Jun 6, 2009

### Andrew Mason

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

4. Jun 7, 2009

### science.girl

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

For (B):
rl.bhat says to "Find ym 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.

Last edited: Jun 7, 2009
5. Jun 7, 2009

### Redbelly98

Staff Emeritus
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.

6. Jun 8, 2009

### science.girl

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?

7. Jun 8, 2009

### Redbelly98

Staff Emeritus
(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?

8. Jun 10, 2009

### science.girl

Perfect! Thank you.