Figure P 18.68 shows a meter stick lying on the bottom of a 100-cm -long tank with its zero

step 1 In this question, we have a middle long tank. Okay, and then there's a meter rule. Here, a meter

Figure P 18.68 shows a meter stick lying on the bottom...

Figure $\mathrm{P} 18.68 \quad$ shows $\quad \mathrm{a}$ meter stick lying on the bottom of a $100-\mathrm{cm}$ -long tank with its zero mark against the left edge. You look into the tank at a $30^{\circ}$ angle, with your line of sight just grazing the upper left edge of the tank. What mark do you see on the meter stick if the tank is (a) empty, (b) half full of water, and (c) completely full of water?

Figure $\mathrm{P} 18.68 \quad$ shows $\quad \mathrm{a}$ meter stick lying on the bottom of a $100-\mathrm{cm}$ -long tank with its zero mark against the left edge. You look into the tank at a $30^{\circ}$ angle, with your line of sight just grazing the upper left
edge of the tank. What mark do you see on the meter stick if the tank is (a) empty, (b) half full of water, and (c) completely full of water?

Key Concepts

Apparent Depth

The concept of apparent depth explains how objects submerged in a medium like water appear to be shifted from their real positions when viewed from above. Due to the refraction of light at the interface between water and air, the position of the object seems closer to the surface than it actually is, affecting where the object is observed.

Ray Diagrams in Geometric Optics

Ray diagrams are visual tools used in geometric optics to analyze the paths light rays take as they interact with different surfaces and media. They help in understanding how the observer's line of sight, the positions of objects, and the angles of refraction contribute to the apparent displacement of objects in various scenarios.

Refraction

Refraction is the bending of light as it passes from one medium to another with a different optical density or refractive index. This bending occurs because the speed of light changes between media, causing the light ray to change direction at the interface between materials like air and water.

Snell's Law

Snell's Law quantitatively relates the angles of incidence and refraction to the refractive indices of the two media. It is expressed by the equation n? sin?? = n? sin??, where n? and n? are the refractive indices of the first and second media and ?? and ?? are the angles of incidence and refraction, respectively. This law is critical in determining the path of light as it crosses boundaries.

Transcript

00:02 In this question, we have a middle long tank.

00:07 Okay, and then there's a meter rule.

00:17 Here, a meter stick is at the bottom of the tank.

00:26 And the tank is 50 cm deep.

00:36 So the line of sight is at a 30 degree angle from the horizontal.

00:41 Okay and so in in this question there are three parts so in part a we want to find so basically we want to find a mark on the meter stick that you can see okay when the tank is empty when the tank is half empty and so on okay all right so so, and in part c is completely full water.

01:28 So in part a, when the tank is empty, okay, so we have this triangle.

01:52 Okay, so this is 30 degrees, and then this is 50 cm, and then we want to find x.

01:59 Okay, so, now, so this is basically using the fact that light travels in a straight line.

02:08 So that's the reason why.

02:10 Why we just look at this triangle because light will travel along this hypotenuse okay so we have tangent 30 degrees is equal to 50 cm divided by x so x is equal to 50 cm divide by tangent 30 degrees and you get 87 cm okay so this is the answer in part a then in part b when the tank is half full.

03:05 So we have this situation.

03:10 So since there is water, then we expect some refraction to take place.

03:17 So this is our situation.

03:20 This is our water line.

03:26 Then this is our 30 degree angle from the top.

03:35 From the top of the tank.

03:37 So this is 0 .25 or 25 cm.

03:46 Okay.

03:48 And then there's another 25 cm.

03:53 Then we expect we know that the light will get reflected.

03:58 Okay.

03:58 So there will be two distance that we need to find.