Question

Example 7 (Concave Mirrors) A 10 (cm) tall object is placed in front of a concave mirror with diameter 40 (cm) In four cases (case 1 to case 4) of placing the object at case 5 (cm), 10 (cm), 15 (cm) and 25 (m). Describe the image as following: 1- Position of the image in respect to mirror (the distance of image from mirror) 2- What is the height of image? Is the object magnified or reduced? 3- Is the image real or virtual (image is front or in the back of mirror)? 4- Find the distance between object and image? 5- Draw object/image/mirror diagram.

Answer 1

Given,

h = 10 cm ; d = 40cm

R = D/2 and F = R/2

F = D/4 = 40/4 = 10 cm

We know from lens eqn

1/f = 1/i + 1/o

i = o x f/(o - f)

o = 5 cm

1)i = 5 x 10/(5 - 10) = -10 cm

i = 10 cm (from the mirror)

2)M = -i/o = h'/h

h' = 10/5 x 10 = 20 cm

h' = 20 cm

3)The image is Virtual

4)D = 5 + 10 = 15 cm

D = 15 cm

o = 10 cm

1)i = 10 x 10/(10 - 10) = infinity

i = infinity

2)udefined

3)virtual

4)infinite

o = 15 cm

1)i = 15 x 10/(15 - 10) = 30 cm

i = 30 cm

2)h' = -30/15 x 10 = 20 cm

h' = 20 cm

3)Real

4)D = 15 + 30 = 45 cm

o = 25 m = 2500 cm

1)i = 2500 x 10/(2500 - 10) = 10 cm

i = 10 cm

2)h' = 10/2500 x 10 = 0.04 cm

h' = 0.04 cm

3)REAL

4)D = 2500 + 10 = 2510 cm

D = 2510 cm