The cross-section of a reflecting surface is represented by the equation x² + y² = R² as shown in the figure. A ray travelling in the positive x-direction is directed toward positive y-direction after reflection from the surface at point M. The coordinate of the point M on the reflecting surface is

A tennis ball hits the floor with a speed v at an angle $$\theta $$ with the normal to the floor. If the collision is inelastic and the coefficient of restitution is $$\varepsilon $$, what will be the angle of reflection?

An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the object in between the object and the convex mirror such that it covers lower half of the convex mirror. What should be the distance of the plane mirror from the object, so that there will be no parallax between the images formed by the two mirrors?

A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the vessel is thus formed 20 cm above the lens. If now water is poured in the vessel upto a height of 64 cm, what will be the approximate new position of the image? Assume that refractive index of water is 4/3.