# Constructive interference of monochromatic light

In summary: The condition for constructive interference is that the waves must be of the same frequency. The phase difference between the waves is related to the path difference between the waves.

## Homework Statement

A source S of monochromatic light and a detector D are both located in air a distance h above a horizontal plane sheet of glass, and are separated by a horizontal distance x. Waves reaching D directly from S interfere with waves that reflect off the glass. The distance x is small compared to h so that the reflection is at close to normal incidence.
a). Show that the condition for constructive interference is $\sqrt{x^2+4h^2}-x=(m+\frac{1}{2})\lambda$, and the condition for destructive interference is$\sqrt{x^2+4h^2}-x=m\lambda$. (Hint: Take into account the phase change on reflection.)

## Homework Equations

1.$d\sin\theta=m\lambda$ for constructive interference
2.$d\sin\theta=(m+\frac{1}{2})\lambda$ for destructive interference
3.$\phi=\frac{2\pi}{\lambda}(r_2-r_1)$ phase difference related to path difference

## The Attempt at a Solution

I have tried to find d as
$d=\sqrt{h^2+(\frac{x}{2})^2}$
and the phase difference as
$\phi=\frac{2\pi}{\lambda}(\sqrt{h^2+(\frac{x}{2})^2}-x)$
but i do not know how this related to the equations (b) 1 and (b) 2

Last edited:
Hi,

have you made a drawing of the problem? Analyze the geometry.

Hint: What does the condition for constructive interference mean?
What's the general formula for it?

What are equations (b)1 and (b)2?

Note: The formulas that you listed in "Relevant equations" are for interference when light is incident on slits. But your problem is not about slits.

sorry , not (b)1 and (b)2,
it should be from relevant equations.
As you said, am i necessary to derive other equations
for this problem?
And then following the method as when light is incident on slits
to derive the equations for this problem?

The problem asks you to derive the "condition for constructive interference".
How is this condition defined in general? (It has something to do with path difference.)

Then, make a drawing, because then you can calculate the path difference.

You don't need the equations for the slit.

then , no other equations can be used?
What I need is to derive it myself by that drawing?

## 1. What is constructive interference of monochromatic light?

Constructive interference of monochromatic light is a phenomenon that occurs when two waves of the same frequency and phase overlap, resulting in a higher intensity of light. This happens when the crests and troughs of the waves align with each other, causing them to reinforce each other instead of cancelling out.

## 2. What is monochromatic light?

Monochromatic light is light that consists of a single wavelength or color. It is also referred to as "pure" light because it does not contain a mixture of different wavelengths.

## 3. How does constructive interference affect the color of monochromatic light?

Constructive interference does not change the color of monochromatic light, but it can increase its brightness. The color of light is determined by its wavelength, which remains the same during constructive interference. However, the intensity of the light may increase depending on the degree of interference.

## 4. What is the difference between constructive and destructive interference?

Constructive interference occurs when two waves of the same frequency and phase overlap and reinforce each other, resulting in a higher intensity of light. Destructive interference, on the other hand, occurs when the crests of one wave align with the troughs of another, causing the waves to cancel each other out and resulting in a decrease in intensity.

## 5. What are some practical applications of constructive interference of monochromatic light?

Constructive interference of monochromatic light has many practical applications. It is used in optics, such as in laser technology, to create a highly intense and focused beam of light. It is also used in various imaging techniques, such as holography and interferometry, to produce high-resolution images. Additionally, constructive interference is utilized in many everyday objects, such as anti-reflective coatings on eyeglasses and interference filters in cameras and telescopes.

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