Answer
Verified
424.8k+ views
Hint: We need to understand the image formation by the lenses when the object is placed at a point away from the lens. The position of the object determines the image position, the size of the image and the nature of the image formed due to the object.
Complete step-by-step answer:
We know that a converging lens forms the image of an object placed in front of it by converging the light rays falling on it. We can find the image distance very easily using the lens’ formula when the focal length and the object distance of the system is given.
According to the lens’ formula –
\[\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\]
Where, f is the focal length of the lens,
v is the image distance,
u is the object distance.
It is given that the object is 25 cm away from the lens and the focal length of the lens is 10 cm. We can find the image distance by substituting the values as –
\[\begin{align}
& \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\
& \Rightarrow \dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u} \\
& \Rightarrow v=\dfrac{uf}{u+f} \\
& \Rightarrow v=\dfrac{(-25cm)(+10cm)}{-25+10} \\
& \therefore v=+\dfrac{50}{3}cm=+16.67cm \\
\end{align}\]
We can find the magnification of the image formed by finding the ratio between the image distance to the object distance. This is given by –
\[\begin{align}
& m=\dfrac{v}{u} \\
& \Rightarrow m=\dfrac{\dfrac{50}{3}}{-25} \\
& \therefore m=-\dfrac{2}{3} \\
\end{align}\]
From this we can conclude that the image is two-third of the object size. The image size can be given as –
\[\begin{align}
& h'=mh \\
& \Rightarrow h'=-\dfrac{2}{3}(5) \\
& \therefore h'=-\dfrac{10}{3}cm=3.33cm \\
\end{align}\]
The image size has a negative sign, this implies that the image formed is real and inverted.
The image is formed 16.67 cm away from the lens. The image size is 3.33 cm. The image is real and inverted.
This is the required solution.
Note: The converging lenses need not to convex lenses. A concave lens when submerged in a medium with greater refractive index means that the material of the lens can also act as a converging lens. We should not be confused by this while solving problems.
Complete step-by-step answer:
We know that a converging lens forms the image of an object placed in front of it by converging the light rays falling on it. We can find the image distance very easily using the lens’ formula when the focal length and the object distance of the system is given.
According to the lens’ formula –
\[\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\]
Where, f is the focal length of the lens,
v is the image distance,
u is the object distance.
It is given that the object is 25 cm away from the lens and the focal length of the lens is 10 cm. We can find the image distance by substituting the values as –
\[\begin{align}
& \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\
& \Rightarrow \dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u} \\
& \Rightarrow v=\dfrac{uf}{u+f} \\
& \Rightarrow v=\dfrac{(-25cm)(+10cm)}{-25+10} \\
& \therefore v=+\dfrac{50}{3}cm=+16.67cm \\
\end{align}\]
We can find the magnification of the image formed by finding the ratio between the image distance to the object distance. This is given by –
\[\begin{align}
& m=\dfrac{v}{u} \\
& \Rightarrow m=\dfrac{\dfrac{50}{3}}{-25} \\
& \therefore m=-\dfrac{2}{3} \\
\end{align}\]
From this we can conclude that the image is two-third of the object size. The image size can be given as –
\[\begin{align}
& h'=mh \\
& \Rightarrow h'=-\dfrac{2}{3}(5) \\
& \therefore h'=-\dfrac{10}{3}cm=3.33cm \\
\end{align}\]
The image size has a negative sign, this implies that the image formed is real and inverted.
The image is formed 16.67 cm away from the lens. The image size is 3.33 cm. The image is real and inverted.
This is the required solution.
Note: The converging lenses need not to convex lenses. A concave lens when submerged in a medium with greater refractive index means that the material of the lens can also act as a converging lens. We should not be confused by this while solving problems.
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
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Which are the Top 10 Largest Countries of the World?
One cusec is equal to how many liters class 8 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The mountain range which stretches from Gujarat in class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths