Answer
Verified
430.5k+ views
Hint To solve this we must know the formula of the magnification of mirror and the mirror formula of the concave mirror. Where we will get the relation between the object distance and the image distance from the mirror which we can further use in the mirror formula to find position of object.
Complete step by step solution
Given
Image is three times the size of object.So,
$m = 3$
Where m is the magnification of a mirror.
Magnification: It is the ratio of image distance to the object distance. As the object is always above the principal axis, the height of the object is always positive.
$R = 36cm$
Where R is radius of curvature
We can find the focal length as focal length is the half of radius of curvature
So
$f = \dfrac{R}{2} = - 18cm$
Focal length is negative because it is concave mirror
$f$ is the focal length of the mirror
Also
$m = - \dfrac{v}{u}$
Where m is the magnification of the mirror,
v is the distance of the image from the mirror
u is the distance of the object from the mirror
As $m = 3$ (given)
Therefore,
$v = - 3u$
Now as we know the mirror formula for concave mirror is
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Using the relation $v = - 3u$ and putting value of focal length we get,
$\Rightarrow$ $\dfrac{1}{{ - 3u}} + \dfrac{1}{u} = \dfrac{1}{{ - 18}}$
$\Rightarrow$ $\dfrac{{ - 1 + 3}}{{3u}} + \dfrac{1}{u} = \dfrac{1}{{ - 18}}$
$\Rightarrow$ $\dfrac{2}{{3u}} = \dfrac{{ - 1}}{{18}}$
$\Rightarrow$ $3u = - 36$
$\therefore$ $u = - 12cm$
Hence the position of the object is $12cm$ in front of the mirror
Note Remember while solving the problem always consider the correct sign conventions. Sign conventions are different for the different mirrors. In the case of the lens, the mirror formula can not be used, in this case lens formula is only used.
Complete step by step solution
Given
Image is three times the size of object.So,
$m = 3$
Where m is the magnification of a mirror.
Magnification: It is the ratio of image distance to the object distance. As the object is always above the principal axis, the height of the object is always positive.
$R = 36cm$
Where R is radius of curvature
We can find the focal length as focal length is the half of radius of curvature
So
$f = \dfrac{R}{2} = - 18cm$
Focal length is negative because it is concave mirror
$f$ is the focal length of the mirror
Also
$m = - \dfrac{v}{u}$
Where m is the magnification of the mirror,
v is the distance of the image from the mirror
u is the distance of the object from the mirror
As $m = 3$ (given)
Therefore,
$v = - 3u$
Now as we know the mirror formula for concave mirror is
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Using the relation $v = - 3u$ and putting value of focal length we get,
$\Rightarrow$ $\dfrac{1}{{ - 3u}} + \dfrac{1}{u} = \dfrac{1}{{ - 18}}$
$\Rightarrow$ $\dfrac{{ - 1 + 3}}{{3u}} + \dfrac{1}{u} = \dfrac{1}{{ - 18}}$
$\Rightarrow$ $\dfrac{2}{{3u}} = \dfrac{{ - 1}}{{18}}$
$\Rightarrow$ $3u = - 36$
$\therefore$ $u = - 12cm$
Hence the position of the object is $12cm$ in front of the mirror
Note Remember while solving the problem always consider the correct sign conventions. Sign conventions are different for the different mirrors. In the case of the lens, the mirror formula can not be used, in this case lens formula is only used.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE