# Concave mirror equation calculation

• synergix
In summary, a physics student is trying to obtain a real and virtual image, each 3 times as large as the original object, using a concave mirror with a 0.50 m radius of curvature. The equation used is 1/do + 1/di = 1/f. After some calculations, the student incorrectly obtains a value of d=0.10m, but upon review, realizes the mistake and correctly solves for d=0.25m. The student also notes that since the object is inside the focal point, only a virtual image would be formed.

## Homework Statement

A physics student wants toobtain a real and virtual image that each is 3 times as large as the original object she has a concave mirror with a 0.50 m radius of curvature. what object distance will she require to obtain the real image?

## Homework Equations

1/do + 1/di = 1/f

## The Attempt at a Solution

m = 3 = -di / do 3do = -di

1/d + 1/3d =1/0.25

[1/d + 1/3d =1/0.25]3d

2d + 1 = 3d/0.25

[2d + 1 = 3d/0.25]0.25

0.5d + 0.25 = 3d

2.5d= 0.25

d= .10m m =do huh? I know I did something wrong

based upon my ray diagram do= .32m ish
and if that was the do then there would not be a real image formed becaues the object is inside of the focal point so only a virtual image would be formed right?

since m = 3 = -di / do 3do = -di

I tried to make di negative and that didnt turn out either I am not sure what I have done wrong

1/d + 1/3d =1/0.25
Write this step as
1/d + 1/3d = 4 and solve for d

after looking at the problem today I see that I subtracted d from 3d instead of divided. what a silly mistake lol o well thanks anyways.

## What is the concave mirror equation?

The concave mirror equation is a mathematical formula used to calculate the relationship between the focal length, object distance, and image distance of a concave mirror. It is represented as 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

## How do I calculate the focal length of a concave mirror using the equation?

To calculate the focal length, you need to measure or know the object distance (do) and image distance (di). Then, plug these values into the concave mirror equation and solve for f. Make sure to use consistent units for all measurements, such as meters or centimeters.

## Can the concave mirror equation be used for any concave mirror?

Yes, the concave mirror equation can be used for any concave mirror, as long as the mirror follows the laws of reflection. This includes concave mirrors with different sizes and shapes.

## What is the difference between a real and virtual image in concave mirrors?

A real image is formed when the reflected rays actually converge at a point, while a virtual image is formed when the reflected rays only appear to converge at a point. Real images can be projected onto a screen, while virtual images cannot.

## How does the object distance affect the image distance in concave mirrors?

The object distance directly affects the image distance in concave mirrors. As the object distance increases, the image distance decreases, and vice versa. This is because the concave mirror equation shows an inverse relationship between the two distances.