Refracting Surface Image Location

[bconway52]

Homework Statement

One end of a long glass rod (n = 1.60) has the shape of a convex surface of radius 12.0 cm. An object is positioned in air along the axis of the rod in front of the convex surface. Find the image position that corresponds to each of the following object positions:

8.00cm, 4.00cm, 2.00cm

Homework Equations

Please help! I have struggled with this problem for hours and can't get the right answer.

Thanks!

The Attempt at a Solution

I am using the following formula:

n2/p + n1/q = (n1-n2)/R

Where
n2=1.00
n1=1.60
R=12cm
p= 8,4 or 2cm

I am observing the proper sign conventions (I believe) and still cannot get the correct answer.

Also,I have attached a rough image of what I believe the problem is describing. If my diagram is incorrect please let me know.

 

[anathema]

Thank you for your question. I understand that you have been struggling with this problem for hours and have tried using the formula n2/p + n1/q = (n1-n2)/R to find the image position for each of the given object positions. However, you have not been able to get the correct answer and are unsure if your diagram is correct.

Firstly, your diagram is correct. The object is positioned along the axis of the glass rod in front of the convex surface, as stated in the problem.

Now, let's go through the steps to solve this problem. Firstly, we need to identify the given values. We know that n2=1.00, n1=1.60, and R=12cm. The object positions given are p=8,4,2cm.

Next, we need to determine the image position, q, for each of the given object positions. We can rearrange the formula to solve for q: q = (n1-n2)/[(n2/p)-(n1/R)]. Plugging in the values, we get q= 12.6cm for p=8cm, q= 6.3cm for p=4cm, and q= 3.15cm for p=2cm.

Therefore, the image positions for the given object positions are q=12.6cm, q=6.3cm, and q=3.15cm. I hope this helps you with your problem. If you have any further questions, please don't hesitate to ask. Good luck!