**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* separates a bright
line at 24.5 degrees. 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*

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 must the lens be so that it can resolve objects of 2 *mm*
and thus read a news paper? Assume the light has a wavelength of
400 *nm*.

Solution:

Diffraction limits the resolution
according to **q** = 1.22 **l****/*** D*
=

* D*
= 12.2