How Does a Concave Mirror and Refractive Liquid Affect Image Distance?

[luiseduardo]

Homework Statement

An object is placed at a distance p = 25 cm from a concave mirror of focal length f = 10 cm. About the mirror is poured a small amount of liquid whose refractive index n = 1.4. Determine the distance of the image formed by this optical system to the mirror.

Homework Equations

i think:
f = p.p'/p + p'
d'/d = nobserv./nobject

The Attempt at a Solution

Hello,
I tried to solve this problem, but I'm confused about the answer. I found 14 cm, but I think that my solution isn't right. So .. could anyone explain me how to solve this problem and the final answer ?
Thanks.

 

[anathema]

Thank you for your question. To solve this problem, we can use the mirror equation: 1/f = 1/p + 1/q, where f is the focal length, p is the object distance, and q is the image distance. We can also use the magnification equation: m = -q/p, where m is the magnification.

First, we need to convert the object distance from centimeters to meters, so p = 0.25 m. Then, we can plug in the given values into the mirror equation: 1/10 cm = 1/0.25 m + 1/q. Solving for q, we get q = 0.0833 m.

Next, we can use the magnification equation to find the magnification of the image: m = -0.0833/0.25 = -0.333. This means that the image is inverted and one-third the size of the object.

To find the distance of the image from the mirror, we can use the relationship between the object and image distances in a concave mirror: d'/d = nobserv./nobject. Plugging in the given values, we get d'/0.0833 = 1.4/1. This gives us a value of d' = 0.1167 m.

Therefore, the distance of the image from the mirror is 11.67 cm.

I hope this helps! Let me know if you have any further questions.