Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is π. The difference of resultant intensities, at the point A and B, will be_______I.
Correct Answer: 24
Approach Solution - 1
To solve the problem, we need to evaluate the resultant intensities at points A and B where two light beams interfere. The given intensities are 4I and 9I; these represent the intensities of the individual light beams.
Step 1: Calculate Resultant Intensity at Point A
At point A, the phase difference ϕ = 0, meaning the waves are in phase. The formula for resultant intensity Ires when two coherent beams interfere is: Ires = I1 + I2 + 2√(I1 I2) cos ϕ.
Substituting I1 = 4I, I2 = 9I, and cos(ϕ) = cos(0) = 1:
Ires,A = 4I + 9I + 2√(4I * 9I)
= 13I + 12I = 25I.
Step 2: Calculate Resultant Intensity at Point B
At point B, the phase difference ϕ = π, meaning the waves are out of phase. Use the same formula but with cos(ϕ) = cos(π) = -1:
Ires,B = 4I + 9I + 2√(4I * 9I) * (-1)
= 13I - 12I = 1I.
Step 3: Determine the Difference of Resultant Intensities
The difference between the intensities at points A and B is:
ΔI = Ires,A - Ires,B = 25I - 1I = 24I.
The computed intensity difference ΔI = 24I fits within the expected range of 24,24. Hence, the difference of resultant intensities, at points A and B, is 24I.
Approach Solution -2
\(I_A = (\sqrt{I_1} + \sqrt{I_2})^2 = 25I\)
\(I_B = (\sqrt{I_1} - \sqrt{I_2})^2 = I\)
So,\(I_A - I_B = 25I - I\)
\(= 24I\)
So, the answer is 24.
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Concepts Used:
Photoelectric Effect
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
- h is Planck’s constant.
- ν is the frequency of the incident photon.
- W is a work function.
- E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
- The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
- There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
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