Mirror Formula Calculations

Descartes’ Formula

oi ddf

111

di = distance from mirror to image or objectdo = distance from mirror to the object

Distances behind the mirror are negative

3

Application of Descartes’ formula

Question 1An 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.

Answer: to calculate di

1/f = 1/di + 1/do 1/di = 1/f – 1/do

= ¼ cm – 1/12 cm1/di = 1/6 cm

di = 6 cm

5

Distances to virtual images are negative when using Descartes’ formula!

To calculate magnification

o

i

o

i

d

d

h

hm

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. c) Draw a ray diagram to prove your answer.

Answer: to find hi

m = di/do = 6cm/12cm

= 1/2 = hi/ho

hi = ½ ho = ½ x 2 cmhi = 1 cm

9

Application

Question 2A 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 answer.

10

More Mirror Formulae Newton’s Formula is an alternative formula

to use:

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.

2fSS oi

Magnification can be calculated from the formula

f

S

S

f

h

hm i

oo

i

12

ApplicationQuestion 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 answer.

Find the position of the image.

13

Now use Newton’s Formula!

So = do – f = 8cmSi = f2/So = (4cm)2/(8cm) = 2 cm from focal point…and thus 6 cm from the mirror

m = f/so = 4cm/8cm = 1/2

b) Find the image’s height.

m = hi / ho thus hi = m ho = ½ (2cm) = 1 cmThus both formulae give the same answers!!!!

14

Application

Question 4While 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.