Two coherent beams of wavelength 5000 overset° A reaching a point would individually produce intensities 1.44 and 4.00 units. If they reach there together, the intensity is 10.24 units. Calculate the lowest phase difference with which the beams reach that point.

Question

Two coherent beams of wavelength 5000 overset° A reaching a point would individually produce intensities 1.44 and 4.00 units. If they reach there together, the intensity is 10.24 units. Calculate the lowest phase difference with which the beams reach that point. (A) zero (B) (π /4) (C) (π /2) (D) π

Tardigrade Admin · Accepted Answer

Resultant intensity at the point where the two coherent beam reach together is given by

I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ

\Rightarrow 10.24 = 1.44 + 4.00 + 2 1.44 \times 4.00 cos ϕ

\Rightarrow 10.24 = 5.44 + 4.8 cos ϕ

\Rightarrow cos ϕ = \frac{10.24 - 5.44}{4.8} = 1

\Rightarrow ϕ = 0

Q. Two coherent beams of wavelength $5000 A^{\circ}$ reaching a point would individually produce intensities $1.44$ and $4.00$ units. If they reach there together, the intensity is $10.24$ units. Calculate the lowest phase difference with which the beams reach that point.

$zero$

$\frac{π}{4}$

$\frac{π}{2}$

$π$

Q. Two coherent beams of wavelength 5000A∘ reaching a point would individually produce intensities 1.44 and 4.00 units. If they reach there together, the intensity is 10.24 units. Calculate the lowest phase difference with which the beams reach that point.

zero

4π​

2π​

π

Resultant intensity at the point where the two coherent beam reach together is given by I=I1​+I2​+2I1​I2​​cosϕ ⇒10.24=1.44+4.00+21.44×4.00​cosϕ ⇒10.24=5.44+4.8cosϕ ⇒cosϕ=4.810.24−5.44​=1 ⇒ϕ=0

Q. Two coherent beams of wavelength $5000 A^{\circ}$ reaching a point would individually produce intensities $1.44$ and $4.00$ units. If they reach there together, the intensity is $10.24$ units. Calculate the lowest phase difference with which the beams reach that point.

$zero$

$\frac{π}{4}$

$\frac{π}{2}$

$π$