Exercises: Refraction and Thin Convex Lenses

Define the focal point and focal length of a thin convex lens. What happens to a beam of rays parallel to the principal axis after it passes through the lens?

A thin convex lens has a focal length of $0.20\ \text{m}$. An object is placed $0.60\ \text{m}$ from the lens. Use the thin lens equation $\dfrac{1}{f}=\dfrac{1}{d_o}+\dfrac{1}{d_i}$ to find the image distance.

Classify each image formed by a convex lens as real or virtual and as upright or inverted: (a) an object placed beyond $2f$, and (b) an object placed between the lens and the focal point $f$.

Jayden uses a convex lens with a focal length of $15\ \text{cm}$ to project an image of a candle flame onto a card. The candle is $45\ \text{cm}$ from the lens. (a) Find the image distance. (b) Find the magnification $m=-\dfrac{d_i}{d_o}$. (c) If the flame is $2.0\ \text{cm}$ tall, find the height of its image and state whether it is upright or inverted.

Emma uses a convex lens with $f=10\ \text{cm}$ as a magnifying glass. She holds a coin $6.0\ \text{cm}$ from the lens. (a) Find the image distance, including its sign. (b) State whether the image is real or virtual and upright or inverted. (c) Find the magnification.

A convex lens has a focal length of $12\ \text{cm}$. An object $3.0\ \text{cm}$ tall stands $20\ \text{cm}$ from the lens. Describe how to draw the three principal rays (parallel ray, central ray, focal ray) to locate the image. Then use the thin lens equation to check the image distance and find the image height.

A projector uses a thin convex lens with $f=0.10\ \text{m}$ to put an image of a slide $0.036\ \text{m}$ tall onto a screen. The screen is $4.0\ \text{m}$ from the lens. (a) Find how far the slide must be from the lens. (b) Find the height of the image on the screen and its orientation relative to the slide. (c) Explain why the slide is loaded upside down to make the picture appear upright. (d) The projector is moved so the screen is $8.0\ \text{m}$ away. Must the lens move toward or away from the slide to refocus? Justify your answer.

Mateo places an object on the principal axis of a thin convex lens with $f=8.0\ \text{cm}$ and studies how the image changes as he moves the object. For the object distances $d_o=24\ \text{cm}$, $16\ \text{cm}$, $12\ \text{cm}$, $8.0\ \text{cm}$, and $5.0\ \text{cm}$, determine the image distance (or state that no image forms at a finite distance), and classify each image as real or virtual, upright or inverted, enlarged or reduced. Then explain, using ray diagrams, why the image changes from real to virtual as the object crosses the focal point.