Height = shadow * tan(angle) = 10 * √3 = 5√3 m.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2), 1.5 * sin(45°) = 1 * sin(θ2) => sin(θ2) = 1.5 * 0.7071 = 1.0607, which is not possible, hence total internal reflection occurs.

Since 70° > θc = sin⁻¹(1/1.5) ≈ 41.8°, total internal reflection will occur.

Since the critical angle for glass to air is sin⁻¹(1.00/1.5) ≈ 41.8°, and 60° > 41.8°, total internal reflection occurs.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, n2 = 1.0, and θ1 = 30°. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, leading to θ2 ≈ 48.6°.

Since the angle of incidence (70°) is greater than the critical angle (approximately 41.8° for glass to air), total internal reflection occurs.

Critical angle θc = sin⁻¹(1/1.6) ≈ 38.7°. Since 70° > 38.7°, total internal reflection occurs.

The critical angle for glass to air is sin⁻¹(1/1.5) ≈ 41.8°. Since 70° > 41.8°, total internal reflection will occur.

When the angle of incidence equals the angle of refraction, it indicates that the light is passing from one medium to another of the same optical density, hence they are the same medium.

According to Snell's law, if the angle of incidence equals the angle of refraction, the light is traveling in the same medium, which can be vacuum or air.

At the critical angle, the angle of refraction is 90°, meaning the refracted ray travels along the boundary.

When the angle of incidence equals the critical angle, the light ray is refracted along the boundary at 90°, marking the threshold for total internal reflection.

As the angle increases, the component of gravitational force parallel to the plane increases, which can lead to a decrease in static friction until it reaches its maximum value.

As the angle increases, the component of gravitational force parallel to the plane increases, which can lead to a decrease in static friction until it reaches its maximum value.

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. The largest angle is 4x = 80 degrees.

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180. So, 9x = 180, x = 20. The largest angle = 4x = 80 degrees.

The time period T is given by T = 2π/ω. Therefore, T = 2π/5 = 0.4 s.

L = Iω; if L is doubled and I is constant, then ω must also double.

If angular momentum is conserved, an increase in moment of inertia results in a decrease in angular velocity, and vice versa.

Angular momentum L = Iω; if L is doubled and I remains constant, ω must also double.

Angular momentum is conserved when the net external torque acting on the system is zero.

Zero angular momentum implies no net rotation; particles can still move linearly.

Zero angular momentum does not imply rest; it can be in linear motion.

Centripetal acceleration (a_c) = ω²r. If ω is doubled, a_c becomes (2ω)²r = 4ω²r.

Area = πr^2 => 36π = πr^2 => r^2 = 36 => r = 6.

Area = πr^2 => 50π = πr^2 => r^2 = 50 => r = √50 = 5√2.

Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled, the magnetic flux also doubles.

Magnetic flux Φ is given by Φ = B * A. If the area A is doubled while B remains constant, the magnetic flux also doubles.

Induced EMF is proportional to the area of the loop. If the area is doubled, the induced EMF also doubles.

Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.