Question

30) Size of image of an object by a mirror having a focal lengih of 20 cm iw olxcrved to be reduced to
1/3 of its size. At what distance from the mirror the object has been placed? What is the nature of
image and the mirror.​

Answer 1

Explanation:

Given,

Image size = ⅓ object size

( height of image = ⅓ )

height of object

Focal length = 20 cm

Now;

Lets assume that the mirror is concave , [ focal length of concave mirror is negative]

then;

f = - 20 cm

m = -v = - height of image

u height of object

- v = - ⅓

u

v = u

3

MIRROR FORMULA

1 + 1 = 1 => 1 + 1 = 1

V U F u\3 U - 20

=> 4 = 1

U - 20

U = - 80 cm { as because the sign is negative so the object will be left of the mirror }

V = U

3

V = - 80

3

(the image is real and inverted)

If mirror is convex ( focal length is always positive)

F = + 20 cm

m = height of image

height of object

m = - V

U

V = - U

3

Mirror formula;

1 + 1 = 1 => 1 + 1 = 1

V U F - U\3 U +20

=> - 3 + 1 = 1

U U 20

= > -2 = 1

U 20

U = -40 cm

V = - 40 = + 40

3 3

( image formed is on right side)

(so the nature of the image is virtual and erect)

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