Question

Complete the following ray diagram

Answer 1

Hint: Use the thin lens formula to find the image distance. Use the rules of refraction through the lens to construct the ray diagram.

Formula used: $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$
Here
     $v$ is image distance
     $u$ is object distance
     $f$ is focal length of lens

Complete step by step solution:
As shown in the figure
$\begin{align}
  & f=+F \\
 & u=-\dfrac{3}{2}F \\
\end{align}$
Substituting in the given formula
     $\begin{align}
  & \dfrac{1}{v}=\dfrac{1}{u}+\dfrac{1}{f} \\
 & \dfrac{1}{v}=-\dfrac{2}{3}\dfrac{1}{F}+\dfrac{1}{F} \\
 & \dfrac{1}{v}=\dfrac{1}{3}\dfrac{1}{F} \\
 & v=3F \\
\end{align}$
Therefore, the image will be formed on the opposite side of the lens as that of the object.

Magnification is
     $m=\dfrac{v}{u}=-2$
Therefore, the image will be inverted and twice the size of the object.

The ray diagram can be constructed using the following rules
1. A ray passing parallel to the principal axis will pass through the focus after refraction.
2. A ray passing through the focus will pass parallel to the principal axis after refraction.

A real, inverted and magnified image will be formed as shown below

Note: A convex lens produces a real image when the object is farther than the focus and a virtual image when the object is nearer than the focus. A concave lens always produces a virtual image.