Torque (τ) = F × d × sin(θ) = 15 N × 2 m × sin(90°) = 30 Nm.

When the angle between the transmission axes of two polarizers is 90 degrees, no light passes through, resulting in zero intensity.

When the angle between the transmission axes of two polarizers is 90 degrees, no light is transmitted, resulting in zero intensity.

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25.

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25

If the angle is 90 degrees, A · B = |A||B|cos(90) = 0.

A · B = |A||B|cos(60°) = √(2^2 + 3^2) * √(4^2 + 5^2) * 1/2 = √13 * √41 * 1/2 = 20.

Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.

Height = shadow * tan(angle) = 10 * tan(30) = 10 * (1/√3) ≈ 10 m.

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. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.

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.

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

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. 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.