### Mirror Formula Calculations

```1
f

1
di

1
do
di = distance from mirror to image or
object
do = distance from mirror to the object
Distances behind the mirror are negative
Question 1
An object 2 cm high is placed 12 cm in front of
a concave mirror of focal length 4 cm.
a) Using Descartes’ formula, find the position
of the image.
3
 1/f = 1/di + 1/do



1/di = 1/f – 1/do

1/di = 1/6 cm

di = 6 cm
= ¼ cm – 1/12 cm
Distances to virtual
images are negative
when using Descartes’
formula!
5
m
hi
ho

di
do

From the previous question ‘An object 2 cm
high is placed 12 cm in front of a concave
mirror of focal length 4 cm’.
b) Find the image’s height.

m = di/do = 6cm/12cm


= 1/2 = hi/ho
hi = ½ ho = ½ x 2 cm
 hi = 1 cm
Question 2
A candle flame is located 50 cm in front
of a concave spherical mirror of
a) Find the position of the image.
b) What type of image is formed?
c) What is the magnification of the
image?
d) Draw a ray diagram to prove you
9

Newton’s Formula is an alternative formula to
use:
SiSo 
f
2


Si=distance from focal point to image
So = distance from focal point to object

All distances are positive but care must be
taken calculating Si or So. It is usually
necessary to sketch a ray diagram to check.
10
m 
hi
ho

f
So

Si
f
Question 2
A candle flame is located 50 cm in front of
a concave spherical mirror of radius of
curvature 78 cm.
a) Find the position of the image.
b) What type of image is formed?
c) What is the magnification of the image?
d) Draw a ray diagram to prove you
12
Now use Newton’s Formula!

Find the position of the image.
So = do – f = 8cm
Si = f2/So = (4cm)2/(8cm) = 2 cm from focal point…and
thus 6 cm from the mirror
b) Find the image’s height.
m = f/so = 4cm/8cm = 1/2
m = hi / ho thus hi = m ho = ½ (2cm) = 1 cm
Thus both formulae give the same answers!!!!
13
Question 4
While driving to Taylor’s Mistake, I noticed a convex
mirror on a sharp corner. My 1.2m tall car was 4.0
m away from the mirror and the focal length of the
mirror was 0.60 m.
a) Draw a ray diagram to find the nature (real or
virtual) of the image.
b) Find the position and size of the image formed
using Descartes’ or Newton’s Formulae.
14
```