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: ${\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}={\displaystyle \frac{1}{f}}$
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
$\begin{array}{rl}& f=+F\\ & u=-{\displaystyle \frac{3}{2}}F\end{array}$
Substituting in the given formula
     $\begin{array}{rl}& {\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{u}}+{\displaystyle \frac{1}{f}}\\ & {\displaystyle \frac{1}{v}}=-{\displaystyle \frac{2}{3}}{\displaystyle \frac{1}{F}}+{\displaystyle \frac{1}{F}}\\ & {\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{3}}{\displaystyle \frac{1}{F}}\\ & v=3F\end{array}$
Therefore, the image will be formed on the opposite side of the lens as that of the object.

Magnification is
     $m={\displaystyle \frac{v}{u}}=-2$
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.