The bending of light as it passes into a transparent material of different optical intensity is known as
a. reflection.
b. aberration.
c. refraction.
d. conversion.

The bending of light as it passes into a transparent material of different optical intensity is known as refraction. The correct option among all the options given in the question is option "C".It can never be reflection as reflection is the bouncing of the light from a surface and so option “A” can easily be negated. The last option or option “D” conversion and it mean converting something to another and that means a total change of form. So the last option should also be negated. The second option can also be negated.

The velocity of the cue ball after collision is -2.13 m/s and the velocity of the eight ball after collision is 2.06 m/s

Explanation:

Let m₁ = mass of cue ball = 0.17 kg, m₂ = mass of eight ball = 0.16 kg, v₁ = initial speed of cue ball = 3 m/s, v₂ = initial speed of eight ball = 0 (since it is initially at rest), v₃ = final speed of cue ball, v₄ = final speed of eight ball.

Since the cue ball and eight ball are deflected at an angle to the horizontal, we resolve their final velocity into its components in the x and y direction and then apply it to the law of conservation of momentum.

From the law of conservation of momentum,

In the x- direction

m₁v₁ + m₂v₂ = -m₁v₃cos40 + m₂v₄cos45 (the third quantity is negative since the cue ball moves 40° in the opposite direction)

0.17 × 3 = -0.17v₃cos40 + 0.16v₄cos45

0.51 = -0.130v₃ + 0.113v₄

-0.130v₃ + 0.113v₄ = 0.51 (1)

In the y - direction

0 = m₁v₃sin40 + m₂v₄sin45  (since our initial momentum in the y-direction is zero)

m₁v₃sin40 = -m₂v₄sin45

0.17v₃sin40 = -0.16v₄sin45

0.1093v₃ = -0.113v₄  

v₄ = -0.1093v₃/0.113  (2)

Substituting (2) into (1), we have

-0.130v₃ + 0.113 × -0.1093v₃/0.113  = 0.51

-0.130v₃ -0.1093v₃ = 0.51

-0.239v₃ = 0.51

v₃ = 0.51/-0.239 = -2.134 m/s ≅ -2.13 m/s

Substituting v₃ into (2), we have

v₄ = -0.1093(-2.134)/0.113 = 2.064 m/s ≅ 2.06 m/s

So, the velocity of the cue ball after collision is -2.13 m/s and the velocity of the eight ball after collision is 2.06 m/s