# AP Physics 2 : Magnification

## Example Questions

### Example Question #1 : Optics

An object  tall is  from a mirror. If the image distance is  from the mirror, what is the image height?

Explanation:

The Magnification Equation is as follows:

The negative on the last part is very important. If you don't include it (and it's easy to forget), you will get the wrong answer.

We'll use the parts without  for our problem. We want , so we just need to multiply both sides by .

Now, we can plug in our numbers.

Therefore, the image height is

### Example Question #2 : Magnification

You have a concave mirror and a candle. The candle is  tall, and the image is  tall. What is the the magnification of the mirror?

Explanation:

The magnification equation is

where  is the height of the image, and  is the height of the object. We can plug these given values into the equation.

The magnification is a scalar value, so it's unitless. We can verify this by examining what goes into the equation. Both heights have the same units, which cancel, so that leaves us with no units.

### Example Question #1 : Optics

The image produced by a concave mirror is at , and the magnification is . What is the object distance?

Explanation:

The equation for magnification is

We're given the image distance and the magnification, so we'd use the second equality.

Now, we can plug in our numbers.

The negative in front of the equation is very important. If you forget it, the answer will be incorrect.

The distance from the mirror to the object is . Note that the object distance is always positive.

### Example Question #1 : Optics

An object of height  object is placed  in front of a convex mirror that has a radius of curvature of . Determine the magnification of the image.

None of these

Explanation:

Using the relationship:

Where:

is the object distance from the mirror

is the image distance from the mirror

is the focal length of the mirror

is the radius of curvature of the mirror

Plugging in values:

Solving for :

Using the equation for magnification:

Where:

is magnification

### Example Question #5 : Magnification

You are passing a ray of light through a thin tank of alcohol to determine properties. Assume that the light ray is not effected by the tank's exterior. You find that if a piece of white paper is put underneath the alcohol tank, there is an image on the metal.

Assuming that the image is the size of  and is actually a picture of a tree of size . What can we say about the magnification of this alcohol solution?