A small spotlight mounted in the bottom of a swimming pool that is 4.3 m deep emits light in all directions. On the surface of the pool, directly above the light, the area illuminated is a circle. Determine the maximum radius of this circle. The index of refraction of water is 1.33.

Radius = 4.9m

Explanation:

The critical angle in optics refers to the angle of incidence, beyond which the total internal reflection of light occurs.

The formula for critical angle is;

θ_crit = sin^(-1)(n_r/n_i)

Where:

θ_crit = The critical angle.

n_r = refraction index.

n_i = incident index.

In this case n_i is refraction index of water which is given 1.33

While n_r is the refraction index of air which has a value of 1.

Thus,

θ_crit = sin^(-1)(1/1.33)

θ_crit = 48.75°

In critical angle statements, If the incident ray is precisely at the critical angle, the refracted ray becomes tangent to the boundary at the incidence point and propagates along the interface surface and there is no reflected ray. Thus;

Radius(r) = d.tan θ_crit

Radius = 4.3tan 48.75

Radius = 4.9m

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.