Using the lens formula, we find the image distance to be 40 cm.

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.

Energy consumed can be calculated using E = P * t. Here, P = 60 W and t = 1 hour = 3600 seconds. Thus, E = 60 W * 3600 s = 216000 J.

Energy consumed can be calculated using E = P * t. Here, P = 60 W and t = 2 hours = 7200 seconds. Thus, E = 60 W * 7200 s = 432000 J.

Energy consumed can be calculated using E = P * t. Here, E = 60 W * (5 * 3600 s) = 108000 J.

Energy consumed = Power × Time = 60 W × (2 × 3600 s) = 432000 J.

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.

Critical angle θc = sin⁻¹(1.00/2.42) ≈ 24.4°.

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.

The critical angle for this scenario is approximately 38.7°. Since 50° is greater than the critical angle, total internal reflection occurs.

Since 50° is greater than the critical angle (θc ≈ 41.8°), total internal reflection occurs.

Calculate critical angle: θc = sin^(-1)(1/n) = sin^(-1)(1/1.6) ≈ 38.7°. Since 50° > 38.7°, total internal reflection occurs.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 2.0, θ1 = 45°, and n2 = 1.0 (air). Thus, 2.0 * sin(45°) = 1.0 * sin(θ2) leads to sin(θ2) = √2, which gives θ2 = 90°.

Using sin(θc) = n2/n1, where n1 = 2.42 (diamond) and n2 = 1.0 (air), we find sin(θc) = 1.0/2.42, leading to θc ≈ 24.4°.

Using Snell's law, sin(θc) = n2/n1 = 1.00/2.42. Thus, θc ≈ 24.4°.