Help with double slit physics question?

Question

Monochromatic light falls on two very narrow slits 0.08mm apart. Successive fringes on a screen 6 m away are 4 cm apart. What is the wavelength and frequency of the light?

I'm not sure where to start. My book is very cryptic, and I can't find any equations that use the variables I am given. Any insight would be great. Thanks

Answer 1

(lambda) = ax/D

D being the distance between slits and screen

a being the distances between the maxima and minima of the interferance pattern

x being the slit seperation distance (from the center of the slits)

(Lambda) being the wavelenght of the light.

Then knowing v=f(lambda) and that v = the speed of light, c which a good approximation is 3E8 (3x10^8) m/s then you can find out the wavlenght and frequency.

Remember to keep your units in SI (that is convert cm into meters and 0.08mm into meters)

:)

Answer 2

this is a problem in wave optics involving diffraction; it will matter whether these are bright or dark fringes, but I will deal with that detail later

if you look up the derivation of equations for diffraction, you will see equations of the form:

y= (l L/d)m

where y is the distance of the fringe from the "Central" location on the screen, l is the wavelength of light, L is the distance from the slit to the screen, d is the distance between slits, and m is the order of the fringe; m has an integral value

the equation above is for bright fringes; for dark fringes the equation has a factor of (m+1/2) in place of m

let's assume these are bright fringes.  we know that the y value of one fringe is:

y1=(l L/d)m

and of the successive fringe is:

y2=(l L/d)(m+1)

we are told that the two fringes are 4 cm apart, so we can subtract y1 from y2 and get:

y2-y1=(l L/d)(m+1)-(l L/d)(m)=l L/d = 4 cm

since you know d and L, you can solve for wavelength (l).  Since you know this is light, you get frequency from

c=l f (c=speed of light, f=frequency)

the other trick in these questions is to make sure you use the same set of units for all your distances (so use either m or cm for all your distances)

hope this helps you get started