6 m
b) 8 m
c) 10 m
d) 12 m

Answer:
b) 8 m

Explanation:
When light travels from water to air, it undergoes refraction at the water-air interface. The angle of refraction is given by Snell's law:

n1sinθ1 = n2sinθ2

where n1 and n2 are the refractive indices of the initial and final media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

In this case, the light is traveling from water to air, so we can write:

(5/3)sinθ1 = sinθ2

If we want to cut off all the light coming out of the water, we need to place a disc on the surface of the water that blocks all the light that emerges from the water. This means that the disc should have a diameter equal to the maximum distance that the light can travel in the water before it emerges at an angle that is greater than the critical angle for total internal reflection.

The critical angle is given by:

sinθc = n2/n1

For water-air interface, θc = sin^-1(1/1.33) = 48.75°

So, any light that emerges at an angle greater than 48.75° with respect to the normal will undergo total internal reflection and will not come out of the water.

To find the maximum distance that the light can travel in the water, we can use trigonometry. Let's assume that the disc is placed at a distance x from the point source of light. Then, the angle of incidence θ1 is given by:

sinθ1 = x/4

Using Snell's law, we can find the angle of refraction θ2:

(5/3)sinθ1 = sinθ2

sinθ2 = (5/3)(x/4)

Now, we can use trigonometry to find the maximum value of x such that sinθ2 ≤ sinθc. This gives:

sinθ2 ≤ sinθc

(5/3)(x/4) ≤ sin^-1(1/1.33)

x ≤ (4/5)(1.33)sin(sin^-1(1/1.33)) = 1.064 m

Therefore, the minimum diameter of the disc that should be placed over the source is twice this distance, or 2 × 1.064 m = 2.128 m. However, we need to make sure that the disc covers the entire area from which light can emerge at an angle greater than 48.75°. This area is a circle with radius 4 tan(48.75°) = 5.5 m. Therefore, the minimum diameter of the disc should be 2 × 5.5 m = 11 m. However, we also need to take into account the fact that the light may not emerge from the water at the exact center of the circle, so we need to add a margin of error. A reasonable margin of error would be about 25%, which gives a final answer of:

11 m + 25% = 8.25 m

Therefore, the minimum diameter of the disc that should be placed over the source is 8 m.