Magnification of an image is -2 and an object isplaced at a distance o

1.	Magnification of an image is -2 and an object isplaced at a distance of 20cm from a concavemirror then find the focal length of the mirror
Answer» 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

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

Answer»

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.,

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