Physics, asked by ramsubas007619, 2 months ago

Magnification of an image is -2 and an object is
placed at a distance of 20cm from a concave
mirror then find the focal length of the mirror​

Answers

Answered by BrainlyTwinklingstar
7

Given :

In concave mirror,

Magnification of image = -2

Object distance = - 20cm

To find :

The focal length of the mirror

Solution :

Firstly we have to find image distance using magnification formula that is,

The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign .i.e.,

\boxed{ \bf m = - \dfrac{v}{u} }

where,

  • v denotes image distance
  • u denotes object distance

by, substituting all the given values in the formula,

\dashrightarrow \sf m = - \dfrac{v}{u}

\dashrightarrow \sf  - 2 = - \dfrac{v}{20}

\dashrightarrow \sf  v = 2 \times 20

\dashrightarrow \sf  v = 40 \: cm

Now, using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

\boxed{\bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}

where,

  • v denotes Image distance
  • u denotes object distance
  • f denotes focal length

now, substituting all the given values,

\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}

\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{( - 40)} + \dfrac{1}{( - 20)}

\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{( - 40)}  - \dfrac{1}{ 20}

\dashrightarrow\sf \dfrac{1}{f} = \dfrac{ - 1 - 2}{ 40}

\dashrightarrow\sf \dfrac{1}{f} = \dfrac{ -3}{ 40}

\dashrightarrow\sf f =   - \dfrac{40}{3}

\dashrightarrow\sf f =   - 13.3 \: cm

Thus, the focal length of the mirror is 13.3cm

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