Diffraction

Single-Slit Diffraction Pattern: Distance to the First Minimum

For a single-slit diffraction pattern, the condition for the first minimum (zero intensity) is given by:

Where:

• is the width of the slit,
• is the angle of diffraction,
• is the order of the minimum (for the first minimum, ),
• is the wavelength of the light.

Given Data:

• ,
• ,
• (distance from the slit to the screen).

For the first minimum, , the equation becomes:

Substitute the known values:

Now, for small angles, , so:

Where is the distance from the central maximum to the first minimum on the screen. Thus:

Substituting the values:

Thus, the distance of the nearest point from the central maximum at which the intensity is zero is .

Why You Can Hear but Not See a Person Behind a Wall

The reason you cannot see a person standing on the other side of a boundary wall but can hear them is based on the difference in the wavelengths of light and sound.

Light Waves:

Light waves have very small wavelengths, in the order of nanometers (approximately m). These small wavelengths cannot bend around large obstacles like walls, which are much larger than the wavelength of light. As a result, light waves cast sharp shadows, and you cannot see the person standing behind the wall.

Sound Waves:

Sound waves, on the other hand, have much longer wavelengths, typically in the order of centimeters to meters. These longer wavelengths can diffract around the edges of a boundary, such as a wall, and thus can be heard even though the person is not visible.

This phenomenon is an example of diffraction, where waves spread out and bend around obstacles.