A transparent slab of thickness d has a refractive index n (z) that increases with z. Here, z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n₁ and n₂ (> n₁), as shown in the figure. A ray of light is incident with angle $$\theta$$_i from medium 1 and emerges in medium 2 with refraction angle $$\theta$$_f with a lateral displacement $l$.


Which of the following statement(s) is (are) true?

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is (are) true?

A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.

Taking hc = 1.237 $$\times$$ 10^$$-$$6 eVm and the ground state energy of hydrogen atom as $$-$$ 13.6 eV, the number of lines present in the emission spectrum is