Physics 2000 JAMB Past Questions - Question 19: A boy observes a piece of stone at the bottom of a river 6.0m deep. If he looks from the surface of the river, what is the apparent distance of the stone from him?

Correct Answer

A

Explanation

n=real depth/apparent +depth4/3=6/Apparent+depth ;Apparent depth=4.5mWhen a person observes an object submerged in a fluid, such as water, the apparent distance of the object is different from its actual depth in the fluid due to the refraction of light. To calculate the apparent depth of the stone, you can use Snell's Law.

Snell's Law states:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
- n1 is the refractive index of the medium the light is coming from (air, approximately 1.00).
- θ1 is the angle between the incident ray (from the observer to the object) and the perpendicular line at the interface of the two mediums.
- n2 is the refractive index of the medium the light enters (water, which has a refractive index of about 1.33).
- θ2 is the angle between the refracted ray (inside the water) and the perpendicular line at the interface.

In this case, the observer is looking from the surface of the river (air to water). To find the apparent depth, you need to calculate θ2 and use it to find the distance of the stone from the surface.

1. Let's assume that h is the actual depth of the stone in the river, which is 6.0 meters in this case.

2. You can find θ1, which is the angle between the incident ray and the vertical line. This angle can be found using trigonometry as sin(θ1) = h / d, where d is the horizontal distance from the observer to the stone. Since the stone is at the bottom of the river, d is the same as the apparent depth.

3. Now, use Snell's Law to calculate θ2:
  n1 * sin(θ1) = n2 * sin(θ2)
  1.00 * (h / d) = 1.33 * sin(θ2)

4. Solve for sin(θ2):
  sin(θ2) = (1.00 / 1.33) * (h / d)

5. Now, you can find θ2 by taking the arcsin (inverse sine) of the above value:
  θ2 = arcsin((1.00 / 1.33) * (h / d))

6. The apparent depth (d') is related to the angle θ2 by:
  d' = h / tan(θ2)

7. Substitute the value of θ2 and h to find the apparent depth d'.

Now, you can calculate the apparent distance of the stone from the surface using the apparent depth d' as the depth observed from the surface to the stone. The apparent distance of the stone from the boy when he looks from the surface of the river can be calculated using the concept of apparent depth.

Apparent depth is the perceived depth of an object when viewed from a different medium, such as air to water. It is affected by the refractive index of the medium.

Given:
Actual depth of the stone (h) = 6.0 m

To calculate the apparent distance (d) of the stone from the boy, we can use the formula:

d = h / refractive index

The refractive index of water is approximately 1.33.

Substituting the values into the formula:

d = 6.0 m / 1.33
d ≈ 4.51 m

Therefore, the apparent distance of the stone from the boy, when he looks from the surface of the river, is approximately 4.51 meters.