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Physics 101- Learning Object 9

Side Note:

by looking at the Figure, we can use trigonometry to solve for:

if you notice that the 2 fringes are located too close together ....

you can increase in the space in between...

by either :

keep angle constant, and increase the distance to the screen.

A:

OR

increase the angle with by rearranging:

d sin = m

λ

Ө

B:

λ

to get ...

λ

increase the

angle will decrease

"d" and

increase " "

m

d

sin = -----

Ө

λ

Now that we have solved for "d"

we can achieve this by

setting = 90 degrees

Ө

we want to calculate the MAXIUM number

of fringes on either side

... and solving for "m"

Ө

d sin (2.7 X 10^-6) Sin (90)

(4.73 X 10 ^-7)

m = ------ = ----------------- =

5.71

λ

now we can answer our question:

Ө

How many bright fringes are on the screen?

m = 5.71

This means there are 5 fringes on each side of the central zero-order maximum.

There are 2 sides, and therefore a total

of

10 fringes.

the angle we want

(work in degrees)

0.0057 m

0.0057 m

0.032 m

------- = 0.178 m

tan =

Ө

Plugging information into Equation (28-5) and solve for :

d

d *sin = m

λ

Ө

what do we have now?

Ө

rearrange equation...

m = 1

= tan ^-1 (0.178)

= 10.09 degrees

λ

d = ------ = ---------------

D = 0.032 m

y = 0.0057 m for m=1

= 4.73 X 10^-7 m

λ

m 1 X (4.73 X 10 ^-7)

sin sin (10.09)

Ө

= 10.09 degrees

Ө

= 2.70 X 10 ^-6 m

since D =0.032 m

the adjacent side of

will also be 0.032 m.

Ө

what do we have?

= 4.73 X 10^-7 m

λ

D = 0.032 m

y = 0.0057 m

m = 1

convert from mm --> m :

wavelength:

0.1 cm 0.01 m

1 mm 1 cm

----- X -----

0.000473mm X

= 4.73 X 10 ^-7 m

what do we need to find in order to solve "how many bright fringes are on the screen?" ?

Distances:

convert from km --> m :

0.000032 km X

1000 m

1 km

----- = 0.032 m

d = ?

= ?

Ө

convert from cm --> m:

can be found

through trigonometry

use to find d

Ө

0.01 m

1 cm

0.57 cm X

----- = 0.0057 m

let's begin by ...

converting units

The Question:

A laser beam with a wavelength of 0.000473mm illuminates a double slit and produces an interference pattern on a screen located 0.000032km away. Fringe m=0 and fringe m=1 is separated by a distance of 0.57 cm.

--> How many bright fringes are present on the screen?

28-3 Double-Slit Interference

Jeanny Chang

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