Question

A convex lens is to be used to throw a magnitude image of an object on a screen 10 m from the lens. If the magnification is to be 19, the focal length of the lens is
\[\begin{align}
  & A)0.5cm \\
 & B)0.75cm \\
 & C)0.80cm \\
 & D)0.90m \\
\end{align}\]

Answer 1

Hint:Here in this type of numerical we have to use lens formula for calculation but sometimes results obtained from lens formula are used as here we use the relation of magnification, focal length and image distance for calculating focal length and by default we always considered image formed is real and inverted.

Complete step-by-step solution:
A convex lens always forms a real and inverted image of an object. Since only in one case of a convex lens it forms a virtual and erect image of an object when it is placed in between focus and optical centre.
But here by default we consider that in case of convex lenses real and inverted images of an object forms on screen.
For real image magnification is taken as negative.
So here magnification\[=-19\].
Let us assume magnification is represented by m.
So, \[m=-19\].
For a real image, the image always lies on the other side of the object so the distance of image from lens is taken as positive.
Let us assume the distance of image from lens is represented by v.
\[v=+10m\]
We have to calculate the focal length of the lens.
Let us assume the focal length of the lens is represented as f.
We have to apply the formula of magnification, focal length and image distance.
 \[m=\dfrac{f-v}{f}---Equation(1)\]
Put the value of magnification, focal length and image distance with their proper sign in above equation 1 then we get,
\[-19=\dfrac{f-10}{f}\]
After Simplifying above expression we get,
\[\begin{align}
  & \Rightarrow -19f=f-10 \\
 & \Rightarrow -20f=-10 \\
\end{align}\]
Minus sign from both sides will cancelled out we get ,
\[\begin{align}
  & \Rightarrow 20f=10 \\
 & \Rightarrow f=\dfrac{10}{20} \\
 & \therefore f=0.5m \\
\end{align}\]
Since focal length of convex lens is always taken as positive in numerical and after calculation of this focal length it also comes as positive so it is clear that it is the focal length of convex lens.
So, focal length of convex lens is \[0.5m\]
Focal length is the distance between focus and optical centre of the lens.
Correct Option is A.

Note: Note:Convex lens is also called converging lens because it always converges the light coming towards convex lens and Concave lens is called diverging lens as it always diverges the light coming towards it. Image formed by concave lens is always virtual and erect while image formed by convex lens can be real and virtual both.