Physics tutorial #19

1. A sinusoidal electromagnetic wave of frequency 40.0 MHz travels in free space in the x direction.

a) Determine the wavelength and period of the wave.
b) At some point and at some instant, the electric field has its maximum value of 750 N/C and is
along the y axis. Calculate the magnitude and direction of the magnetic field at this position and
time.
c) Write expressions for the spacetime variation of the components of the electric and magnetic fields
for this wave.

2. Estimate the maximum magnitudes of the electric and magnetic fields of the light that is incident

on this page because of the visible light coming from your desk lamp. Treat the bulb as a point
source of electromagnetic radiation that is 5% efficient at transforming energy coming in by electrical
transmission to energy leaving by visible light (assume 60 W lightbulb and 0.3 m distance from the
bulb to the page).

3. Two mirrors make an angle of 90 degrees with each other. A ray is incident on mirror M

1

at an

angle of 30 degrees to the normal. Find the direction of the ray after it is reected from mirror M

2

.

Can you think of any practical application of similar devices?

4. A small ball floats on the surface of a swimming pool that is 3.0 m deep. On the bottom of the pool,

what is the distance between the point directly below the ball and the ball’s shadow when the sun
is 30 degrees above the horizon? (for water n =

4
3

)

5. What is total internal reflection? Use Snell’s law to find the critical angle for this phenomenon.

6. Yellow light of wavelength λ = 589 nm travels

from a vacuum, through a water layer, and finally
through a thickness of crown glass. The path of
the beam is shown on the figure below. The angle
of incidence at the vacuum-water is 30

◦

. Calcu-

late the angle θ

4

that ray emerging from the glass

surface makes with the normal.

Vacuum n=1

Vacuum n=1

Water n

2

Glass n

3

30

q

3

q

4

q

2

7. A drinking glass is 4 cm wide at the bottom.

When an observer’s eye is placed as shown on
the figure below, the observer sees the edge of
the bottom of the empty glass. When this glass
is filled with water, the observer sees the center
of the bottom of the glass. Find the height of the
glass. (for water n =

4
3

)

Nivas Babu Selvaraj, Maciej Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/