**A. You wish to create an image that is 10 meters from an object.This image is to be inverted and half the height of the…**

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## Question “A. You wish to create an image that is 10 meters from an object.This image is to be inverted and half the height of the…”

A. You wish to create an image that is 10 meters from an

object. This image is to be inverted and half the height of the

object. You wish to accomplish this using one spherical mirror.

What is the focal length f of the mirror that would accomplish this?

Express your answer in meters, as a fraction or to three significant figures.

B. You wish to create an image that is 10 meters from an object.

This image is to be upright and half the height of the object. You

wish to accomplish this using one spherical mirror.

What is the focal length f of the mirror that would accomplishthis?

Express your answer in meters, as a fraction or to threesignificant

figures.

## Answer

To solve the problem, the focal length of the mirror is required.

Find the object distance and image distances from the expression to determine the magnificence of the mirror. Next, use the mirror equation for the focal length.

Next, calculate the object distance and image distance using the magnification equation. Then, calculate the focal length using the mirror equation.

Mirror equation is the relationship between object distance, image distance, and focal length of mirror.

The mirror equation can be expressed in the following:

denotes the object distance, #media_tag_2$ the image distance and @media_tag_3$ the focal length of a mirror.

Magnification refers to the ratio of the image distance to the object’s distance. You can also define magnification as the ratio between the object’s height and the image’s.

represents the magnification of a mirror.

Magnification can also used as:

refers to the object’s height, and $8media_tag_8$ refers to the image’s height.

**(A)**

Expression for magnifying the mirror is

…… (1)

The image should be at least half the height of the object.

Substitute HTMLmedia_tag_10$ to .

The magnification is negative because the image has an inverted view. The image is only half the size of what it actually is.

Substitute HTMLmedia_tag_13$ with HTMLmedia_tag_14$.

Adjust the expression to adjust the image distance of your mirror.

…… (2)

The distance between the object’s image and the object is

indicates the distance between the object (or image) and the object.

Substitute HTMLmedia_tag_19$ with HTMLmedia_tag_20$. The distance between object and image is:

Adjust the expression above; the mirror’s image distance is.

…… (3)

Compare equations (3) and 4.

Rearrange the expression to solve for the object distance.

Substitute HTMLmedia_tag_25$ to in equation (4). The image distance is.

To find the focal length of a mirror’s mirror, use the mirror equation

Substitute HTMLmedia_tag_25$ to

or HTMLmedia_tag_31$ to

.

The focal length of the mirror is

**(B)**

Expression for magnification of a spherical reflection is

…… (4)

The image is upright, and the image’s height is equal to the object’s.

Magnification can be described as:

Substitute HTMLmedia_tag_10$ to .

The magnification is positive because the image is straight.

Adjust the expression above; the image distance is.

You can also represent the expression as:

…… (5)

The positive magnification value signifies that the image and object are on the same side as the mirror.

is the object’s distance from the mirror. The mirror is on both the image and object. They are separated by

.

Substitute HTMLmedia_tag_47$ to

.

Move the expression above.

The distance between images is calculated by

. Image distance is.

The mirror equation can be expressed in the following:

Substitute HTMLmedia_tag_58$ to

or HTMLmedia_tag_60$ to

.

The focal length of the spherical mirrored is.

Part A – Ans

is the focal length of the mirror which produces an inverted image.

## Conclusion

Above is the solution for “**A. You wish to create an image that is 10 meters from an object.This image is to be inverted and half the height of the…**“. We hope that you find a good answer and gain the knowledge about this topic of **science**.