Question

A 4.5 CM needle is placed at 12 CM away from a convex mirror of focal length 15cm. Give the location of the image and the magnification. describe what happen as the needle is moved further from the mirror.

Answer 1

Answer:

Explanation:

Given:-

u = - 12 cm

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 = 4 + 5/60

⇒ 1/v = 9/60

⇒ v = 60/9

⇒ v = 6.7 cm

Magnification, 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, the image moves to the focus, and the size of the image goes on decreasing.

Answer 2

MbR

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QUESTION :

A 4.5 CM needle is placed at 12 CM away from a convex mirror of focal length 15cm.

Give the location of the image and the magnification.

Describe what happen as the needle is moved further from the mirror.

SOLUTION :

From the above Question, we can get the following information...

A 4.5 CM needle is placed at 12 CM away from a convex mirror of focal length 15cm.

So, the given mirror is a convex mirror.

Its focal length is 15 cm.

Object distance , S = 12 cm.

Now we know that :

1 / f = 1 / s + 1 / s '

Where f is the focal length of the mirror.

s is the object distance.

s' is the image distance.

Substituting the required values ,

1 / 16 = 1 / 12 + 1 / s'

Solving,

s' is approximately equal to 6.7 cm.

Now

Magnification { In a Convex mirror } = - s' / s = h1 / h 2

Where h 1 and h 2 are the respective heights of the object.

h 1 = 4.5 cm.

So,

{ 4.5 / h 2 } = { -6.7 / 12 }

=> h 2 = - 2.5 cm.

The negative sign refers to the fact that the image formed is inverted.

Now, the magnification is also less that 1.

So, the image is diminished.

We can conclude that , as the needle is moved away from the mirror, the image becomes diminished .