Answer
402.9k+ views
Hint: Use the mirror equation to derive the position of image. Use the magnification of a mirror formula to obtain the size of the object. Accordingly depict its nature using the sign of the image height.
Formula Used:
The mirror equation
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Where $v$ is the image distance,$u$ is the object distance and $f$ is the focal length.
Also the magnification of mirrors is given by
$m = \dfrac{{ - v}}{u} = \dfrac{{{h_i}}}{{{h_o}}}$
Where $v$ is the image distance,$u$ is the object distance and $f$ is the focal length, $m$ is the magnification, ${h_i}$ is the height of the image and ${h_o}$ is the height of object.
Complete step by step answer:
Given,
$u = - 15cm$ {Using Sign Convention}
$f = - 10cm$ {Using sign convention since focal length of concave mirror is negative}
${h_o} = 1cm$ We can calculate $v$ by using the following equation,
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Substituting the values of $u$ and $f$ in the above equation we get,
$\dfrac{1}{v} + \dfrac{1}{{ - 15}} = \dfrac{1}{{ - 10}}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{1}{{ - 10}} + \dfrac{1}{{15}}$
Taking L.C.M,
$ \Rightarrow \dfrac{1}{v} = \dfrac{{2 - 3}}{{30}}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{{ - 1}}{{30}}$
Taking the reciprocal, we get
$ \Rightarrow v = - 30cm$
Thus the image is formed $30cm$ in front of the mirror.
Now using the equation,
$m = \dfrac{{ - v}}{u} = \dfrac{{{h_i}}}{{{h_o}}}$
We substitute the values here,
$m = \dfrac{{ - ( - 30)}}{{ - 15}} = \dfrac{{{h_i}}}{{1cm}}$
On solving we get,
$m = - 2 = \dfrac{{{h_i}}}{{1cm}}$
Thus the image is twice the size of object.
On solving further we get that,
${h_o} = - 2cm$
The negative sign indicates that the image is virtual and inverted. This is also because the image is formed at the same side of the mirror with the object.
Hence finally, $v = - 30cm$ , $\left| {{h_o}} \right| = 2cm$ and the image is real and inverted.
Note: Do not confuse the mirror formula with the lens formula and write the magnification formula correctly. Also do not forget to use sign convention correctly as it will cause an error in the answer. Take care of the negative sign in the image height.
Formula Used:
The mirror equation
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Where $v$ is the image distance,$u$ is the object distance and $f$ is the focal length.
Also the magnification of mirrors is given by
$m = \dfrac{{ - v}}{u} = \dfrac{{{h_i}}}{{{h_o}}}$
Where $v$ is the image distance,$u$ is the object distance and $f$ is the focal length, $m$ is the magnification, ${h_i}$ is the height of the image and ${h_o}$ is the height of object.
Complete step by step answer:
Given,
$u = - 15cm$ {Using Sign Convention}
$f = - 10cm$ {Using sign convention since focal length of concave mirror is negative}
${h_o} = 1cm$ We can calculate $v$ by using the following equation,
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Substituting the values of $u$ and $f$ in the above equation we get,
$\dfrac{1}{v} + \dfrac{1}{{ - 15}} = \dfrac{1}{{ - 10}}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{1}{{ - 10}} + \dfrac{1}{{15}}$
Taking L.C.M,
$ \Rightarrow \dfrac{1}{v} = \dfrac{{2 - 3}}{{30}}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{{ - 1}}{{30}}$
Taking the reciprocal, we get
$ \Rightarrow v = - 30cm$
Thus the image is formed $30cm$ in front of the mirror.
Now using the equation,
$m = \dfrac{{ - v}}{u} = \dfrac{{{h_i}}}{{{h_o}}}$
We substitute the values here,
$m = \dfrac{{ - ( - 30)}}{{ - 15}} = \dfrac{{{h_i}}}{{1cm}}$
On solving we get,
$m = - 2 = \dfrac{{{h_i}}}{{1cm}}$
Thus the image is twice the size of object.
On solving further we get that,
${h_o} = - 2cm$
The negative sign indicates that the image is virtual and inverted. This is also because the image is formed at the same side of the mirror with the object.
Hence finally, $v = - 30cm$ , $\left| {{h_o}} \right| = 2cm$ and the image is real and inverted.
Note: Do not confuse the mirror formula with the lens formula and write the magnification formula correctly. Also do not forget to use sign convention correctly as it will cause an error in the answer. Take care of the negative sign in the image height.
Recently Updated Pages
The deliquescent among the following is ACaCl2 BFeSO47H2O class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The d electron configurations of Cr2 + Mn2 + Fe2 + class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of ionization of a 01M bromoacetic acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of Hydrolysis of CH3COONH4 is independent class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the full form of AD a After death b Anno domini class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name 10 Living and Non living things class 9 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)