Spherical mirror image height calculator
Multiply the object height by the mirror's magnification and you have the image: a 4 cm object at magnification −1.5 gives an image 6 cm tall, inverted. The sign shows orientation, the size shows scale. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Object height
- 4
- Magnification
- -1.5
- Image height
- -6
- Absolute image height
- 6
- Orientation
- inverted
- Size relation
- enlarged
This spherical mirror image height calculator finds the signed height of an image when you already know the object's height and the mirror's lateral magnification. It applies the direct relation image height equals magnification times object height, then reports both signed and absolute height. The sign identifies whether the image is upright or inverted, while the magnitude shows whether it is enlarged, reduced, or unchanged. Use any length unit, provided you interpret the resulting height in that same unit.
Calculate image height from object height and magnification
A spherical mirror's lateral magnification compares image height with object height. Written symbolically, m equals hi divided by ho, where m is magnification, hi is image height, and ho is object height. Rearranging gives the calculation used here: hi equals m multiplied by ho.
Enter the object's height and the signed magnification, and the calculator returns the signed image height plus its absolute magnitude. For example, an object four centimetres tall with magnification minus one and a half produces an image height of minus six centimetres. The six-centimetre magnitude tells you the physical image size, while the negative sign tells you that the image is inverted relative to the object.
Because magnification has no unit, the output retains the unit used for object height. If object height is entered in millimetres, image height is in millimetres; if it is entered in metres, the result is in metres. The calculator deliberately does not guess or convert units, which keeps the underlying ratio clear and prevents an unstated conversion from changing the result.
Interpret the sign, orientation, and relative image size
The sign of lateral magnification carries optical meaning. A negative magnification produces a negative signed image height and indicates an inverted image. A positive magnification produces a positive signed image height and indicates an upright image.
The absolute value of magnification describes relative size independently of orientation. When its magnitude is greater than one, the image is enlarged; when it is less than one, the image is reduced; and when it equals one, the image has the same height as the object. Keep in mind that these conclusions use signed lateral magnification.
If a source provides only an unsigned magnification magnitude, the calculator can determine size but cannot recover whether the image is inverted without an externally chosen sign.
Use the result with spherical-mirror calculations and experiments
This capability is the final arithmetic step when magnification is already known from a ray diagram, a measured height ratio, or another spherical-mirror calculation. It does not solve the mirror equation from focal length and object distance, and it does not determine magnification from image and object distances. Supply the signed magnification produced by that earlier work, then use this result to check a laboratory observation, finish a homework problem, populate an optics simulation, or validate a generated answer key.
The algorithm is pure and deterministic, with no network request, model, randomness, or current-time dependency. For reliable interpretation, record the unit beside the original object height and preserve the magnification sign when moving values between tools.
What you can do with it
Complete a mirror worksheet
Turn a previously calculated signed magnification and a stated object height into image height, orientation, and relative size.
Check a spherical-mirror lab
Compare the predicted absolute image height with a screen measurement while retaining the sign that describes inversion.
Generate structured optics feedback
Return deterministic numeric values and plain orientation labels for quizzes, simulations, notebooks, or automated answer checking.
FAQ
Why can the calculated image height be negative?
A negative signed height indicates that the image is inverted relative to the object. Its absolute value is the physical height magnitude.
Does this calculator find mirror magnification from focal length?
No. It requires magnification as an input. Use a mirror-equation calculation first if you need to derive magnification from distances.
What unit is the mirror image height given in?
The same unit you used for the object height. Magnification has no unit, so millimetres in means millimetres out and metres in means metres out; nothing is converted behind your back.
How can I tell if the mirror image is enlarged or reduced?
Look at the magnification without its sign. Above 1 the image is larger than the object, below 1 it is smaller, and exactly 1 means both have the same height.
What happens when the magnification is zero?
The image height comes out as zero, and the result says so plainly instead of calling the image upright or inverted, because no meaningful image forms in that case.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/optics/mirror-image-height \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"object_height":4,"magnification":-1.5}'const res = await fetch("https://api.kit.forhosting.com/optics/mirror-image-height", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"object_height": 4,
"magnification": -1.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/mirror-image-height",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"object_height": 4,
"magnification": -1.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/mirror-image-height", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"object_height":4,"magnification":-1.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"object_height":4,"magnification":-1.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/mirror-image-height", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"object_height": 4,
"magnification": -1.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.mirror_image_height",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Interpret the sign, orientation, and relative image size
Magnification equal to zero gives zero image height, which the response labels as zero_height rather than pretending that a meaningful upright or inverted image has been formed. The response therefore includes orientation and size_relation alongside the numeric values. Those labels are convenient for worksheets, automated feedback, and applications that should not make every caller repeat sign logic.
Use the result with spherical-mirror calculations and experiments
Both inputs must be finite numbers, and excessively large inputs or products are rejected so the API never returns Infinity or an unstable value. The same input therefore gives the same structured response in the browser and through the API. Browser use is free, while each successful API request costs $0.002. Validation errors are returned as invalid_input rather than as fabricated numeric results.
Technical questions
What formula calculates image height for a spherical mirror?
Use image_height = magnification × object_height, which is the rearranged definition m = image_height / object_height.
Which unit does the image height use?
It uses the same length unit as object_height because magnification is dimensionless. The calculator does not perform unit conversion.
How much does the image height API cost?
The browser calculator is free. Each successful API request costs $0.002; invalid input is rejected without returning a computed result.