A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refractive index n = $$\sqrt 2 $$. Light undergoes total internal reflection in the prism at the face PR when a has a minimum value of 45°. The angle q of the prism is :

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ($$\lambda $$) of incident light and the corresponding stopping potential (V₀) are given below:

$$\lambda \left( {\mu m} \right)$$	V0(Volt)
0.3	2.0
0.4	1.0
0.5	0.4

Given that c = 3 $$ \times $$ 10⁸ ms^-1 and e = 1.6 $$ \times $$ 10^-19 C, Planck's constant (in units of J-s) found from such an experiment is) :

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load).
The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is :

(Specific heat of water is 4.2 kJ kg⁻¹ K⁻¹ and the density of water is 1000 kg m⁻³)

A plano-convex lens is made of material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away form the lens. Which of the following statement(s) is(are) true?