# Calculating Distance from Mirror for Virtual Image Height of 1.145 cm

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In summary, using the equation Hi/H = -Si/S and the given values of the object's height and distance from the mirror, we can find the radius of curvature of the mirror to be 15.8 cm. To calculate the distance from the mirror for a virtual image with a height of 1.145 cm, we can use the equation 1/S + 1/Si = 2/R = 1/f and solve for S in terms of Si. The focal length, f, can be found using the radius of curvature, R, and is equal to 7.9 cm.
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## Homework Statement

An object whose height is 0.375 cm is at a distance of 10.5 cm from a spherical concave mirror. Its image is real and has a height of 1.145 cm. Calculate the radius of curvature of the mirror.

Correct, computer gets: 1.58e+01 cm

ACTUAL QUESTION
How far from the mirror is it necessary to place the above object in order to have a virtual image with a height of 1.145 cm?

## Homework Equations

1/S + 1/Si = 2/R = 1/f
Hi/H = -Si/S

## The Attempt at a Solution

I am not sure how to relate the equations...Also, I am unsure as to how the image being virtual in the actual question changes things. I know f=R/2 = 7.9cm

## Homework Statement

Using Hi/H = -Si/S find S in terms of Si. Put it in the equation 1/S + 1/Si = 2/R = 1/f with proper sign of S, Si and f. Solve for S.

An object whose height is 0.375 cm is at a distance of 10.5 cm from a spherical concave mirror. Its image is real and has a height of 1.145 cm. Calculate the radius of curvature of the mirror.

The first step in solving this problem is to use the formula 1/S + 1/Si = 2/R to find the radius of curvature (R) of the mirror. We can rearrange this equation to solve for R: R = 2/(1/S + 1/Si).

Next, we need to use the formula Hi/H = -Si/S to relate the image height (Hi) to the object height (H) and the distances of the object (S) and image (Si) from the mirror. We can rearrange this equation to solve for Si: Si = -Hi*S/H.

Now, we can plug in the given values for Hi, H, and S into this equation to solve for Si. Si = -1.145*10.5/0.375 = -32.2 cm.

Since the image is virtual, the distance of the image from the mirror (Si) will be negative. This means that the image is located behind the mirror, which is what we expect for a virtual image.

Finally, we can plug in the values for Si and S into the equation we found for R to solve for the radius of curvature. R = 2/(1/10.5 + 1/-32.2) = 15.8 cm.

Therefore, the radius of curvature of the mirror is 15.8 cm.

To answer the actual question, we can use the formula 1/S + 1/Si = 2/R to solve for the distance of the object from the mirror (S). We can rearrange this equation to solve for S: S = 1/(1/R - 1/Si).

Plugging in the values for R and Si, we get S = 1/(1/15.8 - 1/-32.2) = 7.5 cm.

Therefore, the object must be placed 7.5 cm from the mirror to produce a virtual image with a height of 1.145 cm.

## 1. How do you calculate the distance from a mirror for a virtual image with a height of 1.145 cm?

To calculate the distance from a mirror for a virtual image, you can use the formula: d = h x (2f)/(h - h'), where d is the distance from the mirror, h is the height of the object, f is the focal length of the mirror, and h' is the height of the virtual image. Plugging in the given values, we get: d = 1.145 cm x (2f)/(1.145 cm - 1 cm). Simplifying this equation gives us the distance from the mirror as d = 2.29f cm.

## 2. What is the focal length of a mirror?

The focal length of a mirror is the distance between the mirror and its focal point. It is denoted by the letter 'f' and is a property of the mirror. The focal length determines the size and position of the image formed by the mirror.

## 3. Can the distance from the mirror for a virtual image be negative?

Yes, the distance from the mirror for a virtual image can be negative. A negative distance indicates that the virtual image is formed behind the mirror, i.e. on the same side as the object. This can occur when the object is placed closer to the mirror than the focal length, resulting in a virtual image that is magnified and upright.

## 4. How does the distance from the mirror affect the height of a virtual image?

The distance from the mirror does not affect the height of a virtual image. The height of the virtual image is solely determined by the distance of the object from the mirror and the focal length of the mirror. However, as the distance from the mirror increases, the size of the virtual image may appear to decrease due to the inverse square law of light.

## 5. What is the significance of calculating the distance from a mirror for a virtual image?

Calculating the distance from a mirror for a virtual image is important in understanding the properties of the mirror and the resulting image. It allows us to determine the location, size, and orientation of the virtual image, which is useful in various applications such as optics, photography, and astronomy.

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