The intensity at each slit are equal for a YDSE and it is maximum $I_{max}$ at central maxima. If $I$ is intensity for phase difference $\frac{7\pi }{2}$ between two waves at screen. Then $\frac{I}{I_{max}}$is

In a Young's double slit experiment, the angular width of a fringe is $0.2°$ on a screen placed $1 \mathrm{m}$ away. The wavelength of light used is $600 \mathrm{nm}.$ The angular width of the fringe if the entire set up is immersed is a liquid of refractive index $1.33$ is,

For light waves are represented by 

(i) $y=a_1\sin \omega t$

(ii) $y=a_2\sin \left(\omega t+\varphi \right)$

(iii) $y=a_1\sin 2\omega t$

(iv) $y=a_2\sin 2\left(\omega t+\varphi \right)$

Interference fringes may be observed due to superimposition of