Two coherent light sources having intensity in the ratio 2 x produce an interference pattern. The ratio ( I max - I min / I max + I min ) will be :

Question

Two coherent light sources having intensity in the ratio 2 x produce an interference pattern. The ratio ( I max - I min / I max + I min ) will be : (A) (2 √2 x / x +1) (B) (√2 x/2 x+1) (C) (√2 x / x +1) (D) (2 √2 x /2 x +1)

Tardigrade Admin · Accepted Answer

Given that, (I1/I2)=2 x We know, I max =(√ I 1+√ I 2)2 I min =(√ I 1-√ I 2)2 ∴ ( I max - I min / I max + I min )=(2 √ I 1 I 2/ I 1+ I 2)=(2 √ I 1 / I 2/( I 1) I 2+1)=(2 √2 x /2 x +1)

Q. Two coherent light sources having intensity in the ratio $2 x$ produce an interference pattern.
The ratio $\frac{I _{m a x} - I _{m i n}}{I _{m a x} + I _{m i n}}$ will be :

$\frac{2 2 x}{x + 1}$

$\frac{2 x}{2 x + 1}$

$\frac{2 x}{x + 1}$

$\frac{2 2 x}{2 x + 1}$

Given that, $\frac{I _{1}}{I _{2}} = 2 x$
We know,
$I_{m a x} = (I_{1} + I_{2})^{2} & I_{m i n} = (I_{1} - I_{2})^{2}$
$∴ \frac{I _{m a x} - I _{m i n}}{I _{m a x} + I _{m i n}} = \frac{2 I _{1} I _{2}}{I _{1} + I _{2}} = \frac{2 I _{1} / I _{2}}{\frac{I _{1}}{I _{2}} + 1} = \frac{2 2 x}{2 x + 1}$

Q. Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio Imax​+Imin​Imax​−Imin​​ will be :

x+122x​​

2x+12x​​

x+12x​​

2x+122x​​

Given that, I2​I1​​=2x We know, Imax​=(I1​​+I2​​)2&Imin​=(I1​​−I2​​)2 ∴Imax​+Imin​Imax​−Imin​​=I1​+I2​2I1​I2​​​=I2​I1​​+12I1​/I2​​​=2x+122x​​

Q. Two coherent light sources having intensity in the ratio $2 x$ produce an interference pattern.
The ratio $\frac{I _{m a x} - I _{m i n}}{I _{m a x} + I _{m i n}}$ will be :

$\frac{2 2 x}{x + 1}$

$\frac{2 x}{2 x + 1}$

$\frac{2 x}{x + 1}$

$\frac{2 2 x}{2 x + 1}$