Geometrical OpticsHard
Question
Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at a point A and π at point B. Then the difference between resultant intensities at A and B is
Options
A.2 I
B.4 I
C.5 I
D.7 I
Solution
I(φ) = I1 + 2 + 2
cos φ ......(i)
Here, I1 = I and I2 = 4I
At point A, φ =
∴ IA = I + 4I = 5I
At point B, φ = π ∴ IB = I + 4I - 4I = I
∴ IA - IB = 4I.
Note : Eq. (i) for resultant intensity can be applied only when the source are coherent. In the question it is given that the rays interfere. Interference take place only when the sources are coherent. This is why we applied equation number (i). When the sources are incoherent, the resultant intensity is given by I = I1 + I2.
cos φ ......(i)Here, I1 = I and I2 = 4I
At point A, φ =
∴ IA = I + 4I = 5IAt point B, φ = π ∴ IB = I + 4I - 4I = I
∴ IA - IB = 4I.
Note : Eq. (i) for resultant intensity can be applied only when the source are coherent. In the question it is given that the rays interfere. Interference take place only when the sources are coherent. This is why we applied equation number (i). When the sources are incoherent, the resultant intensity is given by I = I1 + I2.
Create a free account to view solution
View Solution FreeMore Geometrical Optics Questions
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young′s do...The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D1 and D2 be an of minimum deviation ...If the focal length of objective lens is increased then magnifying power of...When a pin is moved along the principle axis of a small concave mirror, the image position coincides with the object at ...An object is placed 40 cm from a concave mirror of focal length 20 cm. The image formed is...