(a) In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm . The first minimum of the pattern falls at $\theta=30^{\circ}$. Calculate the width of the slit.

OR

(b) In a Young's double-slit experiment, two light waves, each of intensity $I_0$, interfere at a point, having a path difference $\frac{\lambda}{8}$ on the screen. Find the intensity at this point.

A transparent solid cylindrical rod (refractive index $\frac{2}{\sqrt{3}}$ ) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle $\theta$.

Prove that, in Bohr model of hydrogen atom, the time period of revolution of an electron in $n^{\text {th }}$ orbit is proportional to $n^3$.

A $p$-type Si semiconductor is made by doping an average of one dopant atom per $5 \times 10^7$ silicon atoms. If the number density of silicon atoms in the specimen is $5 \times 10^{28}$ atoms $\mathrm{m}^{-3}$, find the number of holes created per cubic centimetre in the specimen due to doping. Also give one example of such dopants.