An EM wave from air enters a medium. The electric fields are

$$\overrightarrow {{E_1}} $$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and

$$\overrightarrow {{E_2}} $$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium,

where the wave number k and frequency $$\nu $$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $$\mu $$m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $${\lambda _n}$$, $${\lambda _g}$$ be the de Broglie wavelength of the electron in the n^th state and the ground state respectively. Let $${\Lambda _n}$$ be the wavelength of the emitted photon in the transition from the n^th state to the ground state. For large n, (A, B are constants)