The position of the object is on the place of the question mark.

In summary, the conversation discusses finding the position of an object and image formed by a convex mirror with a focal length of 10cm, given that the image is one quarter the size of the object. The conversation includes the relevant equations and a discussion on solving the problem. The correct solution is u = 30cm and v = 7.5cm, with an additional note to be careful with the sign of v due to the convex mirror. The conversation also includes a request for help and clarification on finding a common denominator when dealing with fractions and numbers.
  • #1
Boxter
8
0

Homework Statement


A convex mirror of focal length 10cm forms an image that is one quarter the size of the object. Find the position of the object and the image.

Homework Equations


-1/f = 1/u + 1/v
m = v/u

The Attempt at a Solution


m = 1/4
f = 10cm
-1/10 = 1/u + 1/0.25u

I think that 1/u + 0.25u is the problem because I can't find the common denominator. The answer to the question is u = 30cm, v = 7.5cm just in case someone thinks I want them to do my homework for me. I just want to understand how to get it. Thanks.
 
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  • #2
Please help someone
 
  • #3
Dude, relax. Getting impatient after just one hour is not going to help you.
By the way, how does telling us that you know the answer prove anything?

Anyway, your last equation looks correct, except that you need to be careful with the sign of v... the mirror is convex, so it's like a negative lens: it will produce an image on the same side as the object. Hence, v = -0.25u.

Correcting that, you just have a problem with your math. Because in principle,
-1/10 = 1/u - 1/0.25u
is a single equation in one unknown (u), so you can easily solve for u.

Hint: multiply through by u.
 
  • #4
I still don't understand. The point I'm trying to make is that I don't know how to get the common denominator when there's a fraction and a number. I just need someone to tell me how.
 
  • #5
OK, you can also combine the two fractions by making a common denominator...

Then can you answer me this: what should be on the place of the question mark in
[tex]\frac{1}{u} = \frac{?}{0.25 \cdot u} [/tex]
 

1. What is a convex mirror?

A convex mirror is a type of curved mirror that bulges outward and reflects light outwards. It has a reflective surface that curves away from the observer, causing light to spread out and appear smaller in size.

2. What is the convex mirror problem?

The convex mirror problem is a physics problem that involves determining the location and size of an object based on its reflection in a convex mirror. This problem is commonly used to demonstrate how convex mirrors can distort the image of an object.

3. What are the characteristics of an image formed by a convex mirror?

An image formed by a convex mirror is always virtual, upright, and reduced in size. It is also located behind the mirror and its distance from the mirror is dependent on the distance of the object from the mirror.

4. How is the image distance calculated in a convex mirror problem?

The image distance in a convex mirror problem can be calculated using the formula: 1/f = 1/do + 1/di, where f is the focal length of the mirror, do is the object distance, and di is the image distance.

5. What is the difference between convex and concave mirrors?

Convex and concave mirrors have opposite curvatures and produce different types of images. A convex mirror curves outward and produces virtual, upright, and smaller images. On the other hand, a concave mirror curves inward and can produce both real and virtual images, depending on the object's position.

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