(B) For coherent sources,the resultant intensity is given by $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$. At the central point,the path difference is

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(B) For coherent sources,the resultant intensity is given by $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$. At the central point,the path difference is zero,so $\phi = 0$. Given $I_1 = I_2 = I_0$,the intensity for coherent sources is $I_{coh} = I_0 + I_0 + 2\sqrt{I_0 I_0} \cos(0) = 4I_0$. For incoherent sources,the phase difference $\phi$ varies randomly with time,so the average value of $\cos \phi$ is $0$. Thus,the resultant intensity for incoherent sources is $I_{incoh} = I_1 + I_2 = I_0 + I_0 = 2I_0$. The ratio of the intensities is $\frac{I_{coh}}{I_{incoh}} = \frac{4I_0}{2I_0} = \frac{2}{1}$.

Class 12 Physics Wave Optics Young's Double Slit Experiment (YDSE)

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In Young's double slit experiment,the two slits act as coherent sources of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same setup,the two slits are of equal amplitude $A$ and wavelength $\lambda$ but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is

IIT 1986 All IIT

AIEEE 2011 All AIEEE

A
$1 : 2$
B
$2 : 1$
C
$4 : 1$
D
$1 : 1$

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Wave Optics

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Young's Double Slit Experiment (YDSE)

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In a Young's double slit experiment,the wavelength of red light is $7.8 \times 10^{-5} \,cm$ and that of blue light is $5.2 \times 10^{-5} \,cm$. The value of $n$ for which $(n+1)^{\text{th}}$ blue bright band coincides with $n^{\text{th}}$ bright red band is ..........

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The distance of the $5^{\text{th}}$ dark fringe from the center is $4 \, mm$. If $D = 2 \, m$ and $\lambda = 600 \, nm$,then the distance between the slits is (in $mm$):

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In Young's double-slit experiment,the distance between the two slits is $2 \times 10^{-3} \, m$ and the distance between the slits and the screen is $2.5 \, m$. The wavelength of the light used ranges from $2000 \, \mathring{A}$ to $9000 \, \mathring{A}$. What wavelength (in $\mathring{A}$) will form a bright fringe at a distance of $10^{-3} \, m$ from the central maximum?

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The Young's double slit experiment is performed in succession using blue light of wavelength $4360 \, \mathring{A}$ and green light of wavelength $5460 \, \mathring{A}$. If the distance of the fourth maximum from the central maximum is $x$,then:

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Light of wavelength $520\, nm$ passing through a double slit produces an interference pattern of relative intensity versus deflection angle $\theta$ as shown in the figure. The separation $d$ between the slits is

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In a Young's double slit experiment,the wavelength of red light is $7.8 \times 10^{-5} \,cm$ and that of blue light is $5.2 \times 10^{-5} \,cm$. The value of $n$ for which $(n+1)^{\text{th}}$ blue bright band coincides with $n^{\text{th}}$ bright red band is ..........

The distance of the $5^{\text{th}}$ dark fringe from the center is $4 \, mm$. If $D = 2 \, m$ and $\lambda = 600 \, nm$,then the distance between the slits is (in $mm$):

The Young's double slit experiment is performed in succession using blue light of wavelength $4360 \, \mathring{A}$ and green light of wavelength $5460 \, \mathring{A}$. If the distance of the fourth maximum from the central maximum is $x$,then:

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