Answer
397.8k+ views
Hint: If a hollow sphere is cut into parts and the outer surface of the cut part is painted, then it becomes a mirror with its inner surface as the reflecting surface. This mirror type is referred to as a concave mirror.
Formula Used: We will use the following formula to find out the solution of this question
Mirror formula
$\dfrac{1}{{\text{f}}} = \dfrac{1}{{\text{v}}} + \dfrac{1}{{\text{u}}}$
And, magnification formula
${\text{m}} = \dfrac{{ - {\text{v}}}}{{\text{u}}}$
Where
\[m\] is the magnification produced by the concave mirror
\[v\] is the image distance
\[u\] is the object distance
\[f\] is the focal length of the concave mirror
Complete Step-by-Step Solution:
The following information is provided to us in the question:
The magnification produced by the concave mirror, \[m = - 3\]
Object distance, \[u = - 20 cm\]
Now, we will use the magnification formula to find out the image distance
${\text{m}} = \dfrac{{ - {\text{v}}}}{{\text{u}}}$
Upon substituting values, we have
\[ - 3 = \dfrac{{ - v}}{{ - 20}}\]
So, we get Image distance, \[v = - 60 cm\]
Now, we will use the mirror formula
$\dfrac{1}{{\text{f}}} = \dfrac{1}{{\text{v}}} + \dfrac{1}{{\text{u}}}$
On substituting the known values, we get
\[\dfrac{1}{f} = \dfrac{1}{{ - 60}} + \dfrac{1}{{ - 20}}\]
On solving, we get
\[\therefore f = - 15 cm\]
So, the focal length of the concave mirror is \[15 cm\]
Hence, the correct option is (B.)
Note: When light strikes and reflects back from the reflecting surface of the concave mirror, it converges at a point. It is also, therefore, known as a converging mirror. A magnified and virtual image is acquired when the concave mirror is positioned very close to the object.
However, if we increase the distance between the object and the mirror, the image size decreases and a real picture is created. The image that the concave mirror creates can be small or large, or it can be real or virtual.
Formula Used: We will use the following formula to find out the solution of this question
Mirror formula
$\dfrac{1}{{\text{f}}} = \dfrac{1}{{\text{v}}} + \dfrac{1}{{\text{u}}}$
And, magnification formula
${\text{m}} = \dfrac{{ - {\text{v}}}}{{\text{u}}}$
Where
\[m\] is the magnification produced by the concave mirror
\[v\] is the image distance
\[u\] is the object distance
\[f\] is the focal length of the concave mirror
Complete Step-by-Step Solution:
The following information is provided to us in the question:
The magnification produced by the concave mirror, \[m = - 3\]
Object distance, \[u = - 20 cm\]
Now, we will use the magnification formula to find out the image distance
${\text{m}} = \dfrac{{ - {\text{v}}}}{{\text{u}}}$
Upon substituting values, we have
\[ - 3 = \dfrac{{ - v}}{{ - 20}}\]
So, we get Image distance, \[v = - 60 cm\]
Now, we will use the mirror formula
$\dfrac{1}{{\text{f}}} = \dfrac{1}{{\text{v}}} + \dfrac{1}{{\text{u}}}$
On substituting the known values, we get
\[\dfrac{1}{f} = \dfrac{1}{{ - 60}} + \dfrac{1}{{ - 20}}\]
On solving, we get
\[\therefore f = - 15 cm\]
So, the focal length of the concave mirror is \[15 cm\]
Hence, the correct option is (B.)
Note: When light strikes and reflects back from the reflecting surface of the concave mirror, it converges at a point. It is also, therefore, known as a converging mirror. A magnified and virtual image is acquired when the concave mirror is positioned very close to the object.
However, if we increase the distance between the object and the mirror, the image size decreases and a real picture is created. The image that the concave mirror creates can be small or large, or it can be real or virtual.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![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)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![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)
10 examples of evaporation in daily life with explanations
![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)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)