Question

Size of image of an object by a mirror having focal length of 20cm is observed to be reduced to 1/3rd of its size. At what distance tthe object has been placed from the mirror? What is the nature and size?

Answer 1

HII!

lets see the answer in cases!1

CASE 1:-  m=-1/3(in case of concave mirror)

f= -20 cm
m= -1/3 =-v/u
v=u/3

1/f= 1/v +1/u .

=> -1/20 = 3/u + 1/ u= 4/u

therefore.,, u = -80 cm.

CASE 2:-

M=+1/3 (IN CASE OF CONVEX MIRROR)

f=+20 cm.

m=+1/3 =-v/u

v=-u/3.

i/f=1/v+1/u.
=> 1/20= -3/4 + 1/4 =-2/4

therefore, u= -40 cm.

hope it helps!!

please mark as brainliest

thank you!!

Answer 2

Answer:

Explanation:

Solution :-

As we know, m = - v/u = h₁/h₂

⇒ - v/u = 1/3 h₂/h₂

⇒ u = - 3v

Applying mirror formula,

1/v + 1/u = 1/f, we get

when f = + 20 cm

⇒ 1/v - 1/3v = 1/20

⇒ 3 - 1/3v = 1/20

⇒ 2/3v = 1/20

⇒ 3v = 2 × 20

⇒ v = 2 × 30/3

⇒ v = 40/3 .. (i)

u = - 3v

By putting v value, we get

⇒ u = - 3 × 40/3

⇒ u = - 40 cm.

Object Distance = - 40 cm

If we take f = - 20 cm, value of u will be + 40 cm which is not possible.

m = - v/v

⇒ m = - 40/3/- 40

⇒ m = + 1/3

⇒ m = 0.33 cm

This implies that the nature of the image is erect and diminished.

Nature of Image = Convex Mirror.