Question

. The focal length of a
concave mirror is 15cm. If the
object distance is 20cm, find
the position of the image.
O v = 50 cm
O V = - 48 cm
O v = - 60 cm
O v = 70 cm​

Answer 1

Answer:

The position of the image is (v) -60.

Answer 2

Required Answer :

→ v = – 60 cm ( Option C )

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Step-by-step explanation :

Here,

As per the provided question, we have :

• Object distance (u) → –20 cm

[ As object is placed to the left side of the mirror, so object distance will be negative. ]

• Focal length (f) → – 15 cm

[ As it is a concave mirror. ]

We have to find out:–

• Position of the image i.e image distance (v)

Calculation :–

By using mirror formula :

★ $\boxed{\sf{ \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}}$

Where,

● f denotes focal length.

● u denotes object distance.

● v denotes image distance

So, by inserting the values, we get :

$\sf {\longrightarrow \dfrac{1}{-15} = \dfrac{1}{v} + \dfrac{1}{-20}}$

$\sf {\longrightarrow - \dfrac{1}{15} = \dfrac{1}{v} - \dfrac{1}{20}}$

$\sf {\longrightarrow \dfrac{1}{v} = -\dfrac{1}{15} + \dfrac{1}{20}}$

$\sf {\longrightarrow \dfrac{1}{v} = \dfrac{-4+5}{60} }$

$\sf {\longrightarrow \dfrac{1}{v} = \dfrac{-1}{60} }$

$\sf {\longrightarrow \dfrac{1}{v} = -\dfrac{1}{60} }$

$\boxed{ \sf \red{\therefore v = -60 \: cm }}$

Henceforth, the position of the image is –60 cm.

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More formulae :

Mirror formula :

★ $\boxed{\sf{ \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}}$

Where,

● f denotes focal length.

● u denotes object distance.

● v denotes image distance

Magnification formula :

★ $\boxed{\sf{ m = \dfrac{h_i}{h_o} }}$

and,

★ $\boxed{\sf{ m =- \dfrac{v}{u} }}$

Where,

● m = magnification

● h_i = height of the image

● h_o = height of the object

Lens formula :

★ $\boxed{\sf{ \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}}}$

Where,

● f denotes focal length.

● u denotes object distance.

● v denotes image distance