The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on a horizontal surface as shown in figure (18-E13). (a) Where should the pin be placed on the axis so that its image is formed at the same place? (b) If the concave part is filled with water (μ =4/3), find the distance through which the pin should be moved so that the image of the pin again coincides with the pin.

Lenses are constructed by a material of refractive index 1.50. The magnitudes of the radii of curvature are 20 cm and 30 cm. Find the focal lengths of the possible lenses with the above specifications.

Consider the situation shown in figure (18-E16). The elevator is going up with an acceleration of 2.00 ms^-2 and the focal length of the mirror is 12.) cm. All the surfaces are smooth and the pulley is light. The mass-pulley system is released from rest (with respect to the elevator) at t=0 when the distance of B from the mirror is 42.) cm. Find the distance between the image of the block B and the mirror at t=0.200 s. Take g= 10 ms^-2

A mass m = 50 g is dropped on a vertical spring of spring constant 500 N m^-1 from a height h = 10 cm as shown in figure (18-E14). The mass sticks to the spring and executes simple harmonic oscillations after that. A concave mirror of focal length 12 cm facing the mass is fixed with its principal axis coinciding with the line of motion of the mass, its pole being at a distance of 30 cm from the free end of the spring. Find the length in which the image of the mass oscillates.

The focal length of a converging lens are f_v and f_r for violet and red light respectively.

A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index μ. The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for t<. Consider only the image by a single refraction.

A particle is moving at a constant speed V from a large distance towards a concave mirror of radius R along its principal axis. Find the speed of the image formed by the mirror as a function of the distance x of the particle from the mirror.

A 5 mm high pin placed at a distance of 15 cm from convex lens of focal length 10 cm. A second lens of focal length 5 cm is placed 40 cm from the first lens and 55 cm from the pin. Find (a) the position of the final image, (b) its nature and (c) its size.

A diverging lens of focal length 20 cm and a diverging mirror of focal length 7.5 cm are placed 5.0 cm apart with their principal axes coinciding. Where should an object be placed so that its image falls on itself?

Consider the situation described in the previous problem. Where should a point source be placed on the principal axis so that the two images form at the same place?

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.