Convex & Concave Ray Diagrams

Convex Lenses

A convex lens is thicker in the middle and thinner at the edges. It is also called a converging lens because it bends parallel rays of light towards a single point.

Principal focus (F): The point where parallel rays of light converge after passing through the lens.

Focal length (f): The distance from the centre of the lens (optical centre) to the principal focus.

Convex lenses can form different types of images depending on the object's distance from the lens:

• Beyond 2F (twice the focal length): Image is real, inverted, smaller than the object, and formed between F and 2F on the opposite side.
• At 2F: Image is real, inverted, same size as the object, and formed at 2F on the opposite side.
• Between F and 2F: Image is real, inverted, larger than the object, and formed beyond 2F on the opposite side.
• At F: No image is formed because rays emerge parallel.
• Between lens and F: Image is virtual, upright, larger than the object, and formed on the same side as the object.

Convex lenses are used in magnifying glasses, cameras, and the human eye to focus light.

For instance, if an object is placed beyond 2F, the rays converge to form a smaller, inverted image between F and 2F.

Concave Lenses

A concave lens is thinner in the middle and thicker at the edges. It is also called a diverging lens because it spreads out parallel rays of light.

Principal focus (F): The point from which rays appear to diverge after passing through the lens (on the same side as the incoming light).

Focal length (f): The distance from the lens to this virtual focus point.

Concave lenses always produce images that are:

• Virtual: The rays appear to come from a point behind the lens.
• Upright: The image is the same way up as the object.
• Smaller: The image is reduced in size compared to the object.
• On the same side as the object: The image cannot be projected onto a screen.

Concave lenses are used in devices like peepholes and some glasses to correct short-sightedness.

Ray Diagram Construction

Ray diagrams help visualise how lenses form images. When drawing ray diagrams for convex and concave lenses, follow these steps:

Drawing principal rays for a convex lens

• Ray 1: Draw a ray parallel to the principal axis from the top of the object. After passing through the lens, it refracts through the principal focus (F) on the other side.
• Ray 2: Draw a ray through the optical centre of the lens. This ray continues straight without bending.
• Ray 3: Draw a ray through the principal focus (F) on the object side. After the lens, this ray emerges parallel to the principal axis.

Note: For GCSE level, drawing two principal rays is sufficient to locate the image accurately. The third ray is optional and can help confirm the image position.

Drawing principal rays for a concave lens

• Ray 1: Draw a ray parallel to the principal axis from the top of the object. After passing through the lens, it diverges as if coming from the principal focus (F) on the same side as the object.
• Ray 2: Draw a ray through the optical centre of the lens. This ray continues straight without bending.
• Ray 3: Draw a ray directed towards the principal focus (F) on the opposite side of the lens. After the lens, this ray emerges parallel to the principal axis.

Note: Two principal rays are enough for GCSE ray diagrams; the third ray is optional for clarity.

The image is located where the refracted rays (or their backward extensions) meet.

Image size and orientation: Measure the image height and compare it to the object height to determine magnification. The image is inverted if upside down and upright if the same way up as the object.

Always use a ruler and pencil to draw neat, accurate ray diagrams to scale. Label the lens, principal axis, focal points (F), object, and image clearly.

For example, if an object is placed between F and 2F of a convex lens, the rays meet beyond 2F to form a real, inverted, magnified image.

Image Characteristics

Real images are formed when refracted rays actually meet. They can be projected onto a screen. Real images formed by convex lenses are inverted.

Virtual images are formed when rays only appear to meet (their extensions meet). They cannot be projected and are upright. Virtual images are formed by convex lenses when the object is inside the focal length, and always by concave lenses.

Magnification (M) is the ratio of image height to object height:

$$M = \frac{\text{Image height}}{\text{Object height}}$$

If $M > 1$, the image is magnified; if $M < 1$, the image is reduced.

Example: If an object is 5 cm tall and the image is 10 cm tall, then $M = \frac{10}{5} = 2$, so the image is magnified.

Orientation: Images can be inverted (upside down) or upright (same way up as the object).

Dependence on object distance: The image’s size, position, and type change depending on how far the object is from the lens, as explained in the convex and concave lens sections.