Ray Optics: Examining Meter Stick in Tank

Click For Summary

Homework Help Overview

The problem involves a meter stick positioned at the bottom of a tank, with the observer viewing it from a specific angle. The discussion focuses on determining the visible marks on the meter stick under different conditions: when the tank is empty, half full of water, and completely full of water. The subject area pertains to ray optics and the principles of refraction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the law of refraction and the geometry of light paths in relation to the observer's angle of view. There are attempts to calculate the visible marks on the meter stick for different tank conditions, with some participants questioning the assumptions about the tank's height and the angle of observation.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have provided calculations for specific parts of the problem, while others express uncertainty and seek clarification on the methodology, particularly regarding the refraction of light at the water's surface.

Contextual Notes

There is a noted lack of information regarding the height of the tank, which is essential for solving the problem. Additionally, participants are interpreting the angle of observation and its implications for the calculations differently.

rayhan619
Messages
75
Reaction score
0

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?


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
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
    jfk.Figure.18.P56.jpg
    7.4 KB · Views: 1,058
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?
 
  • #10
i got a and c right, but not sure how to do part b.
 
  • #11
(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!
 

Similar threads

Replies
1
Views
3K
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
6K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 20 ·
Replies
20
Views
4K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 13 ·
Replies
13
Views
8K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 33 ·
2
Replies
33
Views
23K