In Young's double slit experiment, the width of the second slit is double the width of the first slit. Consequently, the amplitude of the light from the two slits is different. If $I_m$ is the maximum intensity, the resultant intensity $I$ when they interfere with a phase difference of $\phi$ is given by:

In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $\lambda$. The intensity of light falling on slit $1$ is four times the intensity of light falling on slit $2$. Choose the correct choice(s).
$(A)$ If $d = \lambda$, the screen will contain only one maximum
$(B)$ If $\lambda < d < 2\lambda$, at least one more maximum (besides the central maximum) will be observed on the screen
$(C)$ If the intensity of light falling on slit $1$ is reduced so that it becomes equal to that of slit $2$, the intensities of the observed dark and bright fringes will increase
$(D)$ If the intensity of light falling on slit $2$ is increased so that it becomes equal to that of slit $1$, the intensities of the observed dark and bright fringes will increase

In an interference experiment,the $n^{\text{th}}$ bright fringe for light of wavelength $\lambda_1$ $(n=0, 1, 2, 3, \ldots)$ coincides with the $m^{\text{th}}$ dark fringe for light of wavelength $\lambda_2$ $(m=1, 2, 3, \ldots)$. The ratio $\frac{\lambda_1}{\lambda_2}$ is

In $YDSE$ with two identical slits,when the upper slit is covered with a transparent sheet of mica,the second-order minima is observed above the center of the screen and the second-order maxima below it. Which of the following cannot be a possible value of the phase difference caused by the mica sheet?

In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The distance between the two coherent sources is $d$ and $D$ is the distance between the source and the screen. The possible wavelengths used are inversely proportional to

In Young's double-slit experiment,the separation between the two slits is $3 \, mm$ and they are illuminated by light of wavelength $480 \, nm$. The screen is at a distance of $2 \, m$ from the plane of the slits. Find the separation between the $8^{th}$ bright fringe and the $3^{rd}$ dark fringe with respect to the central bright fringe.