Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is

Question

Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is (A) 16: 1 (B) 2: 1 (C) 5: 3 (D) 9: 1

Tardigrade Admin · Accepted Answer

(I max /I min )=((√I1+√I2)2/(√I1-√I2)2), Now I1=4 I2 ⇒ (I max /I min )=((√4+1)2/(√4-1)2)=(9/1)

Q. Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is

16: 1

2: 1

5: 3

9: 1

$\frac{I _{m a x}}{I _{m i n}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}},$
Now $I_{1} = 4 I_{2}$
$\Rightarrow \frac{I _{m a x}}{I _{m i n}} = \frac{( 4 + 1 ) ^{2}}{( 4 - 1 ) ^{2}} = \frac{9}{1}$

Q. Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is

16: 1

2: 1

5: 3

9: 1

Imin​Imax​​=(I1​​−I2​​)2(I1​​+I2​​)2​, Now I1​=4I2​ ⇒Imin​Imax​​=(4​−1)2(4​+1)2​=19​

$\frac{I _{m a x}}{I _{m i n}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}},$
Now $I_{1} = 4 I_{2}$
$\Rightarrow \frac{I _{m a x}}{I _{m i n}} = \frac{( 4 + 1 ) ^{2}}{( 4 - 1 ) ^{2}} = \frac{9}{1}$