**Examples for interference and
diffraction**

Example #1

Problem:

A screen is placed 3.0 *m* from a
two-slit setup with the slits separated by 15 m*m*. If the
wavelength of the light is 4000 *nm*, how far apart are the principal and *m *=
1* *fringes?

Solution:

First, solve for the angle
**q**
of the maximum using
**l**
= *d *sin**q**,
where * d* is the slit separation. Then, solve for the
position of the fringe,

* y*
= 8

Example #2

Problem:

A diffraction grating with 12 thousand
lines per *cm* creates a bright line at 24.5 degrees away from the central
bright line. What is the wavelength of the light?

Solution:

The separation between slits * d *on
the grating is 1/12,000. Using

**l** = 345.6 *nm*

You could also compute where the next bright line appears...

You could also compute *how many* bright lines appear (based on the
fact that they can't extend beyond 90 degrees)...

Example #3

Problem:

Which of the formulae (* a*
or

a.) 2* t*
= (

1.) Light comes from the vacuum and reflects off a soap film floating in air.

Use formula * a*
because only one reflection is from a lower-to-higher

2.) Light comes from the vacuum and reflects off a soap film floating over glass.

Use formula * b*
because both reflections are from lower-to-higher

3.) Light comes from the glass and reflects off a soap film with vacuum on the other side.

Use formula * b*
because neither reflection is from a lower-to-higher

Example #4

Problem:

Light of wavelength 400 *nm* is
incident on a single slit of width 15 microns. If a screen is placed 2.5 *m *from
the slit, how far is the first minimum from the central maximum?

Solution:

First, solve for the angle **q **of the
minimum using **l**
= *a *sin**q**, where * a*
is the slit wdith. Then, solve for the position of the fringe,

* y*
= 6.67

Example #5

Problem:

A spy satellite travels at a distance of 50
*km* above Earth's surface. How large would the lens have to be so that it
can resolve objects of 2 *mm* and thus read a newspaper? Assume the light
has a wavelength of 400 *nm*.

Solution:

Diffraction limits the resolution according to
**sin** **q**
** = 1.22 **
**l**
**/ D**. We also have

* D*
= 12.2

(This is too large to build, even with military budgets; but only by about one order of magnitude, so presumably they can at least read the headlines.)