Ask Me Help Desk - Constructive interference condition.

A thin air gap of thickness d is present between two sheets of glass of thickness L. Suppose m is an integer. The condition for constructive interference within the air gap, in the reflected beam viewed at near-normal incidence is?

I am very confused here. Could you please help

Light will pass through the glass into the thin air gap. Because of the differences in the index of refraction between glass and air, some of it will be reflected backward from the surface of the glass. This will interact with the light coming through the glass. If the thin air gap is certain fraction of the wavelength, there will be destructive interference. This is used in antireflection coatings.

This is called "thin-film interference", and if you Google that, you'll see a wealth of information on it. Here's one source:

Thin Film Reflection and Interference

Oh OK,

I forgot to mention that the question was asking for which formula for constructive interference should be used out of these options. (in this case)? Is it..

a) 2L= (m+1/2)wavelength

b) 2d= (m+1/2)wavelength

c) 2d= m.wavelength

d) dsin(angle)= (m+1/2)wavelength

e) tan(angle)= 1/(n1)wavelength.

What multiple of its initial intensity I0 does the intensity of an electromagnetic wave change to if the amplitude of its electric field increases from E0 to 2E0?
In this question, for example, if the intensity doubles your answer would be 2).

The following data resulted from measurements on a rectangle: width = 29 ± 0.5 cm, breadth = 34 ± 0.5 cm. Calculate the area of the rectangle and its uncertainty in cm2:

A cylinder is measured and found to be 27 m long and 33 m in diameter.

1. What is the radius of the cylinder? Would that be half of the diameter?
2. What is the volume of the cylinder in m3? Cm2

The volume of a cylinder is where R is the radius and L is the length.

I'm sure if I did your homework for you, you wouldn't learn much and I'm sure you don't want that.

The questions on a rectangle and cylinder are pretty trivial. The others aren't that bad, either. Try them out and post your answers. Tell us why you chose what you did. If you have trouble. We'll tell you where you went wrong.

Hints:

Remember that in the thin air gap case, if light travels an integral number of wavelengths and then joins with incoming light, everything will be in phase and you will get constructive interference. If light travels half a wavelength, you will get destructive interference.

$radius\, of\, a\, circle\, = \pi \,\times\,diameter$

volume of a cylinder = area of the face of a cylinder times the height, h (or length, if you wish), of the cylinder.

$V_c=ah=\pi r^2h$

Area of a rectangle = width x height. There are several ways to calculate uncertainty and I'm not sure which you're being taught. One method is to calculate the percentage uncertainty for each measurement. ADD the percentage uncertainties and multiply the sum of the percent errors (as a fraction) times the total area, volume, etc.

Ok,

so for this question The following data resulted from measurements on a rectangle: width = 29 ± 0.5 cm, breadth = 33 ± 0.5 cm. Calculate the area of the rectangle and its uncertainty in cm2:

Area would be 957. (does breadth mean height?) and uncertanity is 1cm but in cm^2 would be just be 1cm^2?

Because the question wants me to epxress the answer as ___ ±_____ cm2

width = 29 ± 0.5 cm
breadth = 34 ± 0.5 cm

The fractional error in width is $0.5 \div 29 = 0.01724$

The fractional error in breadth is $0.5 \div 34 = 0.01471$

Add the fractional errors.

$0.01724 + 0.01471 = 0.03195$

Multiply the main values as usual.

$29 \times 34 = 986$

Multiply the fractional error times

$error = 0.03195 \times 986 = 31.5$

Therefore

$29 \pm 0.5 cm\, \times \,34 \pm 0.5 cm = 986 \pm 31.5$

As I mentioned, there are other ways to calculate the error, and some of these may lead to higher or lower estimates of error.

Thanks for that.. And also sorry I had to change slightly some numbers here as because the teacher changed it again. This was the other question I had trouble with.

So, A cylinder is measured and found to be 26 m long and 34 m in diameter. 1. What is the radius of the cylinder?
2. What is the volume of the cylinder in m3? __cm2

Isn't the radius - half of the diameter so 17?

and therefore the volume is v= pi x 17^2 x 26 = 23605.93 would that be in m^3 units.. so then how do I convert this to cm^2?

Could you provide a little hint.
Thanks

Quote:

So, A cylinder is measured and found to be 26 m long and 34 m in diameter.

1. What is the radius of the cylinder?

Isn't the radius - half of the diameter so 17?

First off, the next time you have a separate question, put it in a different thread.

Yup. 17 m.

Quote:

2. What is the volume of the cylinder in m3? __cm2

and therefore the volume is v= pi x 17^2 x 26 = 23605.93 would that be in m^3 units.. so then how do I convert this to cm^2?

Also correct, though I haven't multiplied it out.

Since your radius is in meters, and the length is in meters, the volume is in cubic meters. $m \, \times \, m \, \times \,m\,=\,m^3$

To convert it to cm^3 (not cm^2 -- remember the square of a length is area. The cube of a length is a volume, and therefore volume must be in m^3 or cm^3 or some other length cubed) we do the following:

This is called "dimensional analysis", and it always works (and it's easy). It's a way of changing dimensions if you don't know the exact conversion factor off the top of your head. We know that 100 cm = 1 m (right?)

$m^3 = m^3 \, \times \, (100\, \frac {cm}{m}^3)$

The m^3 cancels out (think of m^3 as $\frac {m^3}{1})$

Note how 100 cm x 100 cm x 100 cm gives you 1000000 cm^3

$m^3 = m^3 \, \times \, 1000000 \frac {cm^3}{m^3}$

$V\, m^3 = V\, m^3 \, \times \, 1000000 \, \frac {cm^3}{m^3}\,=\,V\, cm^3$

So, looking at the equation, to convert m^3 to cm^3, all we have to do is multiply by 1000000 (100^3).