# AP Physics 2 : Mirrors

## Example Questions

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### Example Question #1 : Mirrors

Suppose that an object is placed 15cm in front of a concave mirror that has a radius of curvature equal to 20cm. Will the resulting image be upright or inverted? Will it be a real or virtual image?

Upright and virtual

There is no way to determine whether the image is real, virtual, inverted, or upright based on the information given

Inverted and virtual

Inverted and real

Upright and real

Inverted and real

Explanation:

To solve this problem, it is essential to use the mirror equation:

Where:

is the distance the object is from the mirror

is the distance the image is from the mirror

is the focal length of the mirror

To calculate the focal length, we'll have to use the radius of curvature:

Plugging this value into the top equation and rearranging, we obtain:

Therefore, the image distance is:

Since the image distance calculated above is a positive value, this means that the image forms on the same side of the mirror that the reflected light traveled. Thus, the image is real.

To determine whether the image is inverted or upright, we'll need to use the magnification equation:

The magnification obtained above is a negative number. As a result, the image formed from this scenario will be inverted.

### Example Question #1 : Mirrors

You have an object 17.0cm away from a concave mirror with a focal length of 7.40cm. What is the image distance?

There is not enough information to determine the image distance

Explanation:

Because we're dealing with a mirror, appropriately we would use the Mirror Equation:

where  is the focal length,  is the object distance, and  is the image distance. Because we're trying to solve for , we need to rearrange the equation to solve for it.

Now, we can just plug in our values for  and :

Therefore, the image distance is 13.1cm.

### Example Question #1 : Mirrors

An object is set near a mirror like below.

At which point would the image be?

A

E

B

C

D

A

Explanation:

If you were to draw a line from an object to its image on a flat mirror, the line would be perpendicular to the plane of the mirror. The distance from the image to the mirror would be the same distance from the mirror to the object. Only point A fits both criteria, as all other points aren't perpendicular with the mirror, and point E isn't the same distance either.

### Example Question #2 : Mirrors

You place a candle  away from a concave mirror with a radius of curvature of . What is the image distance?

Explanation:

For this problem, we use the mirror equation, rearraged to find .

is the image location,  is the object location, and  is the focal point which is equal to the radius of curvature. Plugging in our known values:

Therefore, the image distance is  from the mirror. Remember, for concave mirrors, the image is on the same side as the object, and has a flipped orientation.

### Example Question #3 : Mirrors

An object is  from a convex mirror with a radius of . What is the image distance?

Explanation:

For convex mirrors, the mirror equation is slightly different than for concave mirrors.

Note the negative sign in front of the focal point. This is because a convex mirror is the same as a concave mirror pointing in the opposite direction.

Now, we rearrange the equation to solve for .

Now, we can plug in our numbers.

Therefore, the image is at , which is on the concave side of the mirror.

### Example Question #4 : Mirrors

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

Determine the size of the image.

Explanation:

Use the mirror/lens equation:

Where:

is the object distance from the mirror, which is taken to be negative number

is the image distance from the mirror

is the focal length of the mirror, which for convex mirrors is taken to be negative number

is the radius of curvature of the mirror

Plug in values:

Solve for :

Use the equation for magnification:

In this equation:

is magnification

is image height

is object height

Plug in values and solve for :

### Example Question #5 : Mirrors

An object of height  is placed in front of a concave mirror that has a radius of curvature of . Determine the focal length of the mirror.

Explanation:

Use the relationship for concave mirrors:

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

Plug in values:

Solve for :

### Example Question #6 : Mirrors

An object of height  is placed  in front of a convex mirror that has a radius of curvature of

Determine the distance of the image.

Explanation:

Use the mirror/lens equation:

Where:

is the object distance from the mirror, which is taken to be negative

is the image distance from the mirror

is the focal length of the mirror, which is taken to be negative for convex mirrors

is the radius of curvature of the mirror

Plug in values:

Solve for the image distance:

### Example Question #7 : Mirrors

An object of height  is placed  in front of a convex mirror that has a radius of curvature of

Determine the focal length of the mirror.

Explanation:

Use the mirror/lens equation:

Where:

is the object distance from the mirror, which is taken to be negative

is the image distance from the mirror

is the focal length of the mirror, which is taken to be negative for convex mirrors

is the radius of curvature of the mirror

Plug in values:

Solve for the focal length:

### Example Question #8 : Mirrors

An object of height  is placed  in front of a concave mirror that has a radius of curvature of

Determine the magnification of the image.

Explanation:

Use the mirror/lens equation:

Where:

is the object distance from the mirror, which is taken to be negative

is the image distance from the mirror

is the focal length of the mirror, which for concave mirrors is taken to be positive

is the radius of curvature of the mirror

Plug in values:

Solve for the image distance:

Use the magnification equation:

Where

is magnification

is image height

is object height

Plug in values and solve for magnification:

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