# Ray Optics: Examining Meter Stick in Tank

• rayhan619
In summary, the problem involves determining which mark on a meter stick would be visible when looking into a 100-cm-long tank at a 30 degree angle, with varying levels of water in the tank. Part (a) involves using basic trigonometry to find the mark visible when the tank is empty, while part (b) requires using the law of refraction to determine the mark visible when the tank is half full of water. Part (c) is similar to part (b) but involves the tank being completely filled with water. A diagram is necessary to solve the problem accurately.
rayhan619

## Homework Statement

The figure shows a meter stick lying on the bottom of a 100-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.
1)What mark do you see on the meter stick if the tank is empty?
2)What mark do you see on the meter stick if the tank is half full of water?
3)What mark do you see on the meter stick if the tank is completely full of water?

## The Attempt at a Solution

Welcome to PF.

What are your thoughts on how to solve the problem?

im not sure how to start this problem. please help me

Sketch a ray originating at some point on the meter stick, going up the surface at an angle, refracting to a larger/smaller angle as it emerges from the water.

That was just for practise. Now draw a similar ray that goes right into the observer's eye from point x on the ruler. Use the law of refraction to work back from the angle of refraction to the x on the ruler.

i get x = 42.9 cm.
is it right?
how do i do part b and c.
i have attached the picture

#### Attachments

• jfk.Figure.18.P56.jpg
7.4 KB · Views: 999
I can't actually do the problem without knowing the height of the tank and I don't understand "a 30^\circ angle".

i have attached the picture in my previous post. i guess the height is 50 cm. and "a 30^\circ angle" means a 30 degree angle
thank you

The a part has no refraction - the ray is a straight line at 30 degrees to the bottom of the tank. Tan(30) = 50/x When you solve that for x, I don't think you get 42.9. It would have to be greater than 50.

For part (b) - half full - you must do a Law of Refraction formula to see how the angle changes. See http://en.wikipedia.org/wiki/Refraction
Look up the index of refraction for water and for air to put in the formula. Show your work here if you would like a check.

a) tan(30) = 50/x
x = 50/tan(30)
x= 86.6

b) n1 sin(theta1) = n2 sin (theta2)
theta1 = sin^-1 (sin 60*1.00/1.33)
theta1 = 40.63

tan(40.63) = x/50
x = tan (40.63) * 50
x = 42.9

c) is it same as b?
whats the difference between half full and full?

i got a and c right, but not sure how to do part b.

(b) is a bit more complicated because the ray travels at the original angle until it hits the water. You'll have to find the horizontal part of that and add it to the horizontal part traveled at the 40.6 degrees to get the total x. A diagram will be essential!

## 1. What is the purpose of examining a meter stick in a tank for ray optics?

The purpose of examining a meter stick in a tank for ray optics is to observe and study the behavior of light rays as they pass through different mediums, such as air and water. This can help us understand how light behaves and how it can be manipulated, which has practical applications in fields such as optics, photography, and astronomy.

## 2. How does the meter stick in the tank experiment work?

The meter stick in the tank experiment involves placing a meter stick at the bottom of a tank filled with water. A light source is then shone through the water at an angle, and the position of the meter stick is adjusted until the light rays passing through it are parallel. This allows us to measure and analyze the refraction of light as it passes through the water and the meter stick.

## 3. What is the difference between reflection and refraction?

Reflection is when light bounces off a surface, while refraction is when light passes through a medium and changes direction due to the change in speed. Reflection follows the law of reflection, where the angle of incidence is equal to the angle of reflection, while refraction follows Snell's law, which describes the relationship between the angles of incidence and refraction.

## 4. How does the index of refraction affect the behavior of light?

The index of refraction is a measure of how much a medium can slow down the speed of light. The higher the index of refraction, the slower the speed of light through that medium. This affects the behavior of light by causing it to bend or refract as it passes through the medium, as well as changing its direction and potentially its wavelength.

## 5. What are some real-world applications of understanding ray optics?

Understanding ray optics has numerous applications in our daily lives, including the design of lenses for glasses and cameras, the creation of optical instruments like microscopes and telescopes, and the development of fiber optics for communication and data transmission. It also plays a crucial role in fields such as astronomy, where the study of light from distant objects can reveal important information about the universe.

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