Question

Problem-1 : A 4.5 cm candle is placed 12 cm away
from a convex mirror of focal length 15 cm. Give the
location of image and magnification. Describe what
happens to the image as the needle is moved farther
from the mirror.​

Answer 1

Given :-

• Distance of object from the mirror ( u ) = 12 cm .

• Object size = h1 = 4.4 cm.

• Focal length ( f ) = 15 cm .

Solution :-

Using lens formula :-

⇒  1/f = 1/u + 1/v

⇒  1/v = 1/f - 1/u

⇒  1/v = 1/15 - 1/- 12

⇒  1/v = 60/9

⇒  v = 6.7 cm

As we move farther the  image will be diminished as the lens is convex lens.

Image is formed 6.7 CM behind the convex mirror. it must be virtual and erect.

Size of h2 :-

⇒  m = - (- v/u) = h₂/h₁

⇒  m = - 6.7/- 12

⇒  m = 0.558

⇒  m = h₂/h₁

⇒  h₂ = h₁ × m

⇒  h₂ = 0.558 × 4.5

⇒  h₂ = 2.5 cm.

As the needle is moved further from the mirror, image moves to the focus and the size of image goes on decreasing.

★  $\red\large\sf{More\:To\:Know :-}$

✪ h = size

✪ m = magnification.

✪ v = velocity

✪ u = distance

✪ f = focal length

In a convex lens :

• u is always negative.
• f is always positive.
• Hence the lens formula gets altered a bit and we can find the distance by using the magnification formula also.
• We know that the convex lens has negative magnification and hence it always diminishes the image.
• Thus the nature will be diminished.