A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt7$$ m. The refractive index of water is $${4 \over 3}$$. The area of the surface of water through which light from the bulb can emerge out is x$$\pi$$ m². The value of x is __________.

A light ray is incident, at an incident angle $$\theta$$₁, on the system of tow plane mirrors M₁ and M₂ having an inclination angle 75$$^\circ$$ between them (as shown in figure). After reflecting from mirror M₁ it gets reflected back by the mirror M₂ with an angle of reflection 30$$^\circ$$. The total deviation of the ray will be _____________ degree.

A ray of light is incident at an angle of incidence 60$$^\circ$$ on the glass slab of refractive index $$\sqrt3$$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4$$\sqrt3$$ cm. The thickness of the glass slab is __________ cm.

Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is __________ cm.