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S1 and S2 are two coherent point sources of light in the xy plane of points *(0,0) and (0,3) the intensity will be maximum at which coordinates
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S1 and S2 are two coherent point sources of light in the xy plane of p...
The intensity will be maximum at points where the path difference between the two coherent sources is an integral multiple of the wavelength.

Let's assume that the wavelength of light is λ.

The distance between points (0,0) and (0,3) is 3 units.

Now, let's consider a point P(x,y) in the xy plane. The distance between point P and (0,0) is √(x^2 + y^2) and the distance between point P and (0,3) is √(x^2 + (y-3)^2).

The path difference between the two coherent sources at point P is given by:
√(x^2 + (y-3)^2) - √(x^2 + y^2)

For the intensity to be maximum, the path difference should be an integral multiple of the wavelength λ:
√(x^2 + (y-3)^2) - √(x^2 + y^2) = nλ, where n is an integer.

Squaring both sides of the equation, we get:
x^2 + (y-3)^2 - 2√((x^2 + (y-3)^2)(x^2 + y^2)) + x^2 + y^2 = n^2λ^2

Simplifying the equation, we get:
2x^2 + 2y^2 - 2√((x^2 + (y-3)^2)(x^2 + y^2)) - 6y + 9 = n^2λ^2

This equation represents an ellipse. The coordinates (x,y) where the intensity will be maximum are the points on this ellipse.

In conclusion, the intensity will be maximum at the coordinates (x,y) that lie on the ellipse given by the equation 2x^2 + 2y^2 - 2√((x^2 + (y-3)^2)(x^2 + y^2)) - 6y + 9 = n^2λ^2.
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Read the following text and answer the following questions on the basis of the same:In one of his experiments on interference, August Jean Fresnel used a biprism to induce interference between two beams. He split a diverging beam of light into two parts by using the biprism to refract them. This resulted in two split beams which acted as if they were from two coherent sources and which therefore interfered with each other.A Fresnel Biprism is a thin double prism placed base to base and have very small refracting angle ( 0.5°). This is equivalent to a single prism with one of its angle nearly 179° and other two of 0.5° each.In Young’s double Slits experiment, a single source is split in two coherent sources. For the Young’s slits experiment, we must approximate that the slits act as point sources. This however is not the case, since the slits have finite width. In this way, it gives rise to unwanted diffraction effects that causes errors.The Fresnel biprism experiment overcomes this problem.A Fresnel biprism is a variation of Young’s Slits experiment. When monochromatic light through a narrow slit falls on biprism that divides it into two components. One of these component is refracted from upper portion of biprism and the other one refracted through lower portion. Two virtual coherent sources formed from the original source. In this case, two virtual coherent sources are point sources and replace slits in Young’s experiment.Q. Which problem of Young’s double slit experiment is overcome by Fresnel biprism?

Read the following text and answer the following questions on the basis of the same:In one of his experiments on interference, August Jean Fresnel used a biprism to induce interference between two beams. He split a diverging beam of light into two parts by using the biprism to refract them. This resulted in two split beams which acted as if they were from two coherent sources and which therefore interfered with each other.A Fresnel Biprism is a thin double prism placed base to base and have very small refracting angle ( 0.5°). This is equivalent to a single prism with one of its angle nearly 179° and other two of 0.5° each.In Young’s double Slits experiment, a single source is split in two coherent sources. For the Young’s slits experiment, we must approximate that the slits act as point sources. This however is not the case, since the slits have finite width. In this way, it gives rise to unwanted diffraction effects that causes errors.The Fresnel biprism experiment overcomes this problem.A Fresnel biprism is a variation of Young’s Slits experiment. When monochromatic light through a narrow slit falls on biprism that divides it into two components. One of these component is refracted from upper portion of biprism and the other one refracted through lower portion. Two virtual coherent sources formed from the original source. In this case, two virtual coherent sources are point sources and replace slits in Young’s experiment.Q. What is the difference between the coherent sources produced by Young’s double slit arrangement and Fresnel biprism?

Read the following text and answer the following questions on the basis of the same:In one of his experiments on interference, August Jean Fresnel used a biprism to induce interference between two beams. He split a diverging beam of light into two parts by using the biprism to refract them. This resulted in two split beams which acted as if they were from two coherent sources and which therefore interfered with each other.A Fresnel Biprism is a thin double prism placed base to base and have very small refracting angle ( 0.5°). This is equivalent to a single prism with one of its angle nearly 179° and other two of 0.5° each.In Young’s double Slits experiment, a single source is split in two coherent sources. For the Young’s slits experiment, we must approximate that the slits act as point sources. This however is not the case, since the slits have finite width. In this way, it gives rise to unwanted diffraction effects that causes errors.The Fresnel biprism experiment overcomes this problem.A Fresnel biprism is a variation of Young’s Slits experiment. When monochromatic light through a narrow slit falls on biprism that divides it into two components. One of these component is refracted from upper portion of biprism and the other one refracted through lower portion. Two virtual coherent sources formed from the original source. In this case, two virtual coherent sources are point sources and replace slits in Young’s experiment.Q. Fresnel biprism produces

S1 and S2 are two coherent point sources of light in the xy plane of points *(0,0) and (0,3) the intensity will be maximum at which coordinates Related: L11 : Coherent & incoherent source - Wave Optics, Physics, Class 12
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