The cladding has a lower refractive index than the core, ensuring that light is kept within the core through total internal reflection.

Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.

Using the lens formula 1/f = 1/v - 1/u, where u = -60 cm and v = 20 cm, we find f = 30 cm.

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/15 - 1/60. Solving gives f = 10 cm.

Using magnification m = -v/u = 3, we find v = -60 cm and then use the lens formula to find f = 15 cm.

Using the lens formula and magnification, we find the focal length to be 15 cm.

A virtual image is formed by a concave lens when the object is placed within its focal length.

Using the lens formula, 1/f = 1/v - 1/u, we find f = 4 cm.

Using the lens formula 1/f = 1/v - 1/u, where v = -20 cm and u = -10 cm, we find f = 5 cm.

A virtual image formed by a lens indicates that it is a concave lens.

A positive focal length indicates that the lens is a convex lens, which converges light rays.

A negative focal length indicates that the lens is a concave lens.

Since the object distance is greater than the focal length, a real and inverted image is formed.

Power (P) is given by P = 1/f (in meters). Thus, f = 1/P = 1/2 = 0.5 m.

Power (P) = 1/f (in meters), so f = 1/2.0 = 0.5 m = 50 cm.

Power (P) = 1/f (in meters). Therefore, f = 1/2.5 = 0.4 m = 40 cm.

Power (P) = 1/f, so f = 1/P = 1/2.5 = 0.4 m.

Power (P) = 1/f (in meters). Therefore, f = 1/P = 1/5 = 0.2 m = 20 cm.

A negative power indicates a concave lens.

A negative power indicates that the lens is a concave lens.

Magnification (m) = h'/h, thus h' = m * h = 3 * 2 = 6 cm.

A virtual image is formed by a concave lens when the object is placed in front of it.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), n2 = 1.5, i = 30 degrees. Solving gives r = 19.2 degrees.

Since the angle of incidence is less than the critical angle (θc = sin⁻¹(1/1.5) ≈ 41.8°), it will not undergo total internal reflection.

Using Snell's law, n1 * sin(theta1) = n2 * sin(theta2). Here, n1 = 1 (air), n2 = 1.5 (glass), and theta1 = 30 degrees. Thus, sin(theta2) = (1 * sin(30))/1.5 = 0.333, giving theta2 ≈ 19.1 degrees.

When a light ray passes through the center of curvature, it strikes the mirror perpendicularly, resulting in an angle of reflection of 0 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, sin(r) = (1 * sin(45)) / 1.5 = 0.471, giving r ≈ 28 degrees.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), n2 = 1.5 (glass), i = 60 degrees. Solving gives r = 40 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), θ1 = 30 degrees, n2 = 1.5. Thus, sin(θ2) = (1 * sin(30))/1.5 = 1/3, giving θ2 ≈ 20 degrees.

According to the law of reflection, the angle of reflection equals the angle of incidence, so it is 45 degrees.