f

1  1

d i

 1

d o

d i

= distance from mirror to image or object

d o

= 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.

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 

1/f = 1/d

i

1/d

i

+ 1/d = 1/f – 1/d

o o

  

= ¼ cm – 1/12 cm

1/d i = 1/6 cm



d

i

= 6 cm

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

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m



h h o i



d d o i

 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.

 m = d i /d o = 6cm/12cm  = 1/2 = h i /h o  h i = ½ h o = ½ x 2 cm 

h

i

= 1 cm

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 answer.

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 Newton’s Formula is an alternative formula to use:

S i S o



f

2   S i =distance from focal point to image So = distance from focal point to object  All distances are positive but care must be taken calculating S i or S o . It is usually necessary to sketch a ray diagram to check.

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m



h h o i



f S o



S i 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 answer.

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Now use Newton’s Formula!

 Find the position of the image.

S o = d o – f = 8cm S i = f 2 /S o = (4cm) 2 /(8cm) = 2 cm from focal point…and thus 6 cm from the mirror b) Find the image’s height.

m = f/s o = 4cm/8cm = 1/2 m = h i / h o thus h i = m h o = ½ (2cm) = 1 cm Thus both formulae give the same answers!!!!

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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 a) b) mirror was 0.60 m.

Draw a ray diagram to find the nature (real or virtual) of the image.

Find the position and size of the image formed using Descartes’ or Newton’s Formulae.

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