Question

Light of wavelength λ = 595 nm passes through a pair of slits that are 23 μm wide and 185 μm apart. How many bright interference fringes are there in the central diffraction maximum? How many bright interference fringes are there in the whole pattern?

Answer 1

The number of bright interference fringes in the central diffraction maximum is approximately 4. The number of bright interference fringes in the whole pattern is also approximately 4.

Step-by-step explanation:

The number of bright interference fringes in the central diffraction maximum can be determined using the formula:

n = (wavelength * D) / (slit separation)

Where:

• n is the number of interference fringes
• wavelength is the wavelength of light
• D is the distance between the slits and the screen
• slit separation is the distance between the two slits

Substituting the given values, we have:
n = (595 nm * 1.2 m) / (185 um)
n ≈ 3.827
Therefore, there are approximately 4 bright interference fringes in the central diffraction maximum.

To find the number of bright interference fringes in the whole pattern, we can use the formula:

n_max = (2 * wavelength * D) / (slit separation)

Substituting the given values, we have:
n_max = (595 nm * 1.2 m) / (185 um)
n_max ≈ 3.827
Therefore, there are approximately 4 bright interference fringes in the whole pattern.

Answer 2

There are zero bright interference fringes in the central diffraction maximum and zero bright interference fringes in the whole pattern.

Step-by-step explanation:

The number of bright interference fringes in the central diffraction maximum can be found using the formula:

n = (d*sin(theta))/lambda

where n is the number of fringes, d is the distance between the slits, theta is the angle of the fringes, and lambda is the wavelength of the light.

In this case, the distance between the slits is 185 μm and the wavelength is 595 nm. Plugging these values into the formula, we get:

n = (185*10^-6*sin(0))/595*10^-9

n = 0

Therefore, there are zero bright interference fringes in the central diffraction maximum.

To find the number of bright interference fringes in the whole pattern, we can use a similar formula:

N = (D*sin(0))/lambda

where N is the number of fringes, D is the distance between the slits, and theta is the angle of the fringes.

In this case, the distance between the slits is 185 μm and the wavelength is 595 nm. Plugging these values into the formula, we get:

N = (185*10^-6*sin(0))/595*10^-9

N = 0

Therefore, there are zero bright interference fringes in the whole pattern.