To find the value of Imax + Imin / Imax - Imin for the interference pattern of two coherent sources of light with an intensity ratio of 1:9, we can use the concept of superposition of waves.

Let's assume that the intensity of the first source is I1 and the intensity of the second source is I2. Given that the intensity ratio is 1:9, we can write I1:I2 as 1:9.

The total intensity at any point due to the interference of these two sources can be calculated using the principle of superposition. The total intensity, Itotal, is given by the sum of the individual intensities:

Itotal = I1 + I2

Since we know the intensity ratio, we can write I1 as x and I2 as 9x, where x is a constant.

Itotal = x + 9x = 10x

Now, let's consider the maximum and minimum intensities in the interference pattern. The maximum intensity, Imax, occurs when the two sources are in phase and constructively interfere. The minimum intensity, Imin, occurs when the two sources are out of phase and destructively interfere.

For constructive interference, the phase difference between the two sources is an integer multiple of 2π. This means that the path difference between the two sources is an integer multiple of the wavelength of light.

For destructive interference, the phase difference between the two sources is an odd multiple of π. This means that the path difference between the two sources is an odd multiple of half the wavelength of light.

In the interference pattern, the maximum intensity, Imax, occurs when the path difference is zero or an integer multiple of the wavelength. The minimum intensity, Imin, occurs when the path difference is an odd multiple of half the wavelength.

Now, let's calculate the value of Imax + Imin / Imax - Imin.

Imax = Itotal = 10x (since the maximum intensity occurs when the two sources are in phase)
Imin = 0 (since the minimum intensity occurs when the two sources are out of phase)

Therefore, Imax + Imin = 10x + 0 = 10x
Imax - Imin = 10x - 0 = 10x

Now, we can substitute these values into the expression Imax + Imin / Imax - Imin:

(Imax + Imin) / (Imax - Imin) = (10x) / (10x) = 1

So, the value of Imax + Imin / Imax - Imin for the given interference pattern is 1.

Question

To find the value of Imax + Imin / Imax - Imin for the interference pattern of two coherent sources of light with an intensity ratio of 1:9, we can use the concept of superposition of waves.

Let's assume that the intensity of the first source is I1 and the intensity of the second source is I2. Given that the intensity ratio is 1:9, we can write I1:I2 as 1:9.

The total intensity at any point due to the interference of these two sources can be calculated using the principle of superposition. The total intensity, Itotal, is given by the sum of the individual intensities:

Itotal = I1 + I2

Since we know the intensity ratio, we can write I1 as x and I2 as 9x, where x is a constant.

Itotal = x + 9x = 10x

Now, let's consider the maximum and minimum intensities in the interference pattern. The maximum intensity, Imax, occurs when the two sources are in phase and constructively interfere. The minimum intensity, Imin, occurs when the two sources are out of phase and destructively interfere.

For constructive interference, the phase difference between the two sources is an integer multiple of 2π. This means that the path difference between the two sources is an integer multiple of the wavelength of light.

For destructive interference, the phase difference between the two sources is an odd multiple of π. This means that the path difference between the two sources is an odd multiple of half the wavelength of light.

In the interference pattern, the maximum intensity, Imax, occurs when the path difference is zero or an integer multiple of the wavelength. The minimum intensity, Imin, occurs when the path difference is an odd multiple of half the wavelength.

Now, let's calculate the value of Imax + Imin / Imax - Imin.

Imax = Itotal = 10x (since the maximum intensity occurs when the two sources are in phase)
Imin = 0 (since the minimum intensity occurs when the two sources are out of phase)

Therefore, Imax + Imin = 10x + 0 = 10x
Imax - Imin = 10x - 0 = 10x

Now, we can substitute these values into the expression Imax + Imin / Imax - Imin:

(Imax + Imin) / (Imax - Imin) = (10x) / (10x) = 1

So, the value of Imax + Imin / Imax - Imin for the given interference pattern is 1.

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