R1

R2

Synchronous (in phase) waves from two point sources travel different path lengths to reach point A.

A

Point A will experience complete destructive interference if, for some integer m, the path difference =R1-R2

is exactly equal to 1. m2. (m+ ½)3. (m+ 1/4)4. 0

d

=R1-R2

/d = sin

= d sin

Diffraction through a slit

Double-Slit InterferenceDouble-Slit Interference Path difference between waves

determines phase difference

m is an integer: m = 0, ± 1, ± 2, ...

d

L

y

r1

r2

= d sin

For Destructive Interference

= 1/2, 3/2, 5/2, 7/2, …

= (m + 1/2)

d sin = (m + 1/2)

For Constructive Interference = 1, 2 , 3 , 4 , … = m

d sin = m

If is small (r1, r2 >d) then:

The magnetron of a microwave horn generates a horizontally varying B-field and oscillating vertical E-field. We foundwhich of the aluminum gratings below let the microwaves pass?

12

Exposed to Neon laser light passing uninterrupted through a narrowpair of slits, point P is the location of a bright fringe in the resulting interference pattern.

P

If a thin plate of clear crown glass held normal to the path to P covered one of the slits,the point P would

(1) still be a point of constructive interference.(2) be a node (dark fringe) of destructive interference.(3) have a phase difference between the two slits that depended on the thickness of the plate.

Exposed to Neon laser light passing uninterrupted through a narrowpair of slits, point P is the location of a bright fringe in the resulting interference pattern.

P

If a thin sheet of clear crown glass precision ground exactlyto a thickness equal to an oddnumber of wavelengths N is held normal to the path to P covered one of the slits, the point P would

(1) still be a point of constructive interference.(2) become a node (dark fringe) of destructive interference.(3) have a phase difference between the two slits that depended on the number N.

nglass=1.5

A train of waves of fixed frequency is traveling along a thin, light cord toward the juncture to a heavy, thick cord. Both cords are stretched taut and under the same tension.

The waves that travel across the heavy cord will have

1) greater speed than along the lighter cord.2) the same speed as along the lighter cord.3) smaller speed than along the lighter cord.

A train of waves of fixed frequency is traveling along a thin, light cord toward the juncture to a heavy, thick cord. Both cords are stretched taut and under the same tension.

The waves traveling across the heavy cord have

1) larger wavelength than along the lighter cord.2) the same wavelength as along the lighter cord.3) smaller wavelength than along the lighter cord.

Another wayAnother way to get Interference to get Interference

Thin oil film on water: Thin oil film on water:

Part of the incoming light is reflected off the top surface (Part of the incoming light is reflected off the top surface (point Apoint A), part at the lower surface (), part at the lower surface (point Bpoint B).).

Light traveling through oil travels Light traveling through oil travels extra distanceextra distance (from (from A A toto B B toto C C).).

If this distance is If this distance is 223344……

» constructive interferenceconstructive interference!!

If this distance is If this distance is 2233225522……

» destructive interferencedestructive interference!!

A glass (n=1.60) lens is coated with a thin film of fluoride (MgF2, n=1.38).What minimum film thickness makes=550 nm light non-reflecting?

A glass (n=1.60) lens is coated with a thin film of fluoride (MgF2, n=1.38).What minimum film thickness makes=550 nm light non-reflecting?

180o phase changefor each reflection

t=/4

2

12 nt

)38.1(4

550

4

nm

nt

nmt 6.99