To determine if total internal reflection occurs, we first find the critical angle using sin(θc) = 1/n = 1/1.5, which gives θc ≈ 41.8°. Since 60° > 41.8°, total internal reflection will not occur.

Since the angle of incidence (60°) is greater than the critical angle (approximately 41.8° for glass to air), total internal reflection occurs.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Thus, sin(r) = (1 * sin(30)) / 1.5 = 0.333, giving r ≈ 19.1 degrees.

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

According to the diffraction principle, as the slit width decreases, the width of the central maximum increases.

The angle of the first minimum in single-slit diffraction is given by sin(θ) = λ/a, where a is the width of the slit.

The angle for the first minimum in single-slit diffraction is given by a sin θ = λ, hence θ = λ/a.

For a prism, the angle of minimum deviation D is given by D = A(n - 1), where A is the angle of the prism. Here, D = 60(1.5 - 1) = 30 degrees.

For a prism, the angle of minimum deviation (D) can be approximated as D = A for small angles, thus D = 60 degrees.

Using the formula for angle of deviation: D = A(n-1), we find D = 60(1.5-1) = 30 degrees.

Using the lens formula, 1/f = 1/v - 1/u; here, f = 15 cm and u = -30 cm. Thus, 1/v = 1/15 + 1/30 = 1/10, giving v = 10 cm.

According to the law of reflection, the angle of reflection equals the angle of incidence.

According to the law of reflection, the angle of reflection equals the angle of incidence, so it is 60 degrees.

Using the lens maker's formula, f = R/2(n-1). Here, R = 10 cm, n = 1.5, so f = 10/(2(1.5-1)) = 10/1 = 10 cm.

Using the lens maker's formula, the focal length is calculated to be 20 cm.

Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.

Using the lens maker's formula, the focal length is calculated to be 15 cm.

Let the marked price be x. Selling Price = x - 25% of x = 0.75x. Thus, 0.75x = 300, so x = 400.

Percentage of votes = (300/500) * 100 = 60%.

Percentage of votes in favor = (300/500) * 100 = 60%.

Members voting in favor = 55% of 545 = 0.55 * 545 = 299.75, rounded to 300.

Members voting for the bill = 60% of 400 = 240. Members voting against = 400 - 240 = 160.

Members voting in favor = 60% of 545 = 0.6 * 545 = 327.

60% of 545 = 0.6 * 545 = 327 members voted in favor.

A simple majority is more than half, so (545/2) + 1 = 273 votes are needed.

Once the applied force exceeds the maximum static frictional force, the block will start moving.

The maximum angle for static friction is given by tan(θ) = μs. Here, θ = tan⁻¹(0.5) which is approximately 26.57 degrees, so the block can remain at rest at angles less than this.

The block will not slide if the component of gravitational force down the incline is less than or equal to the maximum static friction force, leading to θ = tan⁻¹(μs).

The presence of kinetic friction opposes the motion, thus decreasing the acceleration of the block compared to a frictionless incline.

Frictional force (f_k) = μ_k * N = μ_k * mg = 0.3 * 10 kg * 9.8 m/s² = 29.4 N, approximately 30 N.