Difficulty: Intermediate | Prerequisites: Thin lens equation, mirror equation, sign conventions, basic ray diagrams.
This section tests your conceptual understanding of how optical elements form images. Rather than plugging numbers into equations, you need to reason about which elements can produce real or virtual images, trace rays through multi-lens systems by hand, and predict what appears on a screen when light passes through shaped apertures. These problems reward careful thinking about how light actually travels and are common on exams because they separate students who memorised formulas from those who understand the physics.
A converging lens and a concave mirror can both form real images. A pinhole (or small aperture) acts as a lens-free imaging device: each point on the source sends light through the hole, producing an inverted image of the source on the screen. For extended or shaped light sources with small apertures, the image on the screen is a pattern of overlapping images of the aperture shape, not the source shape.
Pinhole camera (camera obscura)
A dark box with a tiny hole in one wall. Light from each point on a scene passes through the hole and lands on the opposite wall, forming an inverted image. No lens is needed. In simple terms, the hole is so small that only a narrow pencil of rays from each point can pass through, so the image is sharp (though dim).
Ray tracing
The method of drawing specific rays through a lens or mirror to locate the image graphically. For a thin lens, the three principal rays are: (1) a ray parallel to the axis, which refracts through the far focal point; (2) a ray through the near focal point, which refracts parallel to the axis; (3) a ray through the centre of the lens, which passes straight through.
Principal rays
The specific rays used in ray tracing. Any two of the three suffice to locate the image. The third serves as a check.
Real object
An object from which light actually diverges. The standard case: a physical object sitting in front of a lens or mirror.
Virtual object
Occurs in multi-lens systems when the image from the first lens would form behind the second lens. The converging rays heading toward that image act as a virtual object for the second lens. The object distance is negative.
Extended source
A light source with physical size (not a point). When an extended source illuminates a small aperture, every point on the source independently projects an image of the aperture shape onto the screen. The result on the screen is many overlapping copies of the aperture, arranged in the shape of the source.
Which elements can form a real image of a real object?
Converging lens: yes, when the object is beyond the focal point.
Diverging lens: no. A diverging lens always produces a virtual image of a real object.
Concave mirror: yes, when the object is beyond the focal point.
Convex mirror: no. A convex mirror always produces a virtual, reduced, upright image.
If the real image is also enlarged, the choices narrow further:
A converging lens produces an enlarged real image when the object is between f and 2f.
A concave mirror produces an enlarged real image when the object is between f and 2f (the centre of curvature).
Both are still possible. To narrow to one element, you would need additional information (e.g. whether the image is on the same side or opposite side of the element from the object).
The object must be located between f and 2f from the element.
When a diagram shows the image of the first lens, you work backwards to find the object. Use the principal rays in reverse: trace from the image tip back through the lens using the focal points to locate the original object.
For the second lens, the image from lens 1 becomes the object. Draw the standard principal rays from that object through lens 2 to locate the final image.
If the second lens is changed from converging to diverging (same |f|), the final image location and orientation change. A diverging lens always produces a virtual, upright image (relative to its own object), so the combined effect on orientation depends on whether the intermediate image was inverted.
Small point source, shaped aperture (e.g. "F"-shaped hole):
A single point source sends light through every part of the aperture. The screen shows a bright patch in the shape of the aperture (an "F"), inverted top-to-bottom and left-to-right because of the straight-line propagation of light through the hole.
The image size scales with geometry: h_image / h_aperture = (distance from mask to screen) / (distance from source to mask). This is similar-triangle geometry, not the thin-lens equation.
Two point sources (e.g. point source + O-shaped source):
Each source independently projects the shape of the aperture onto the screen. The screen shows two overlapping copies of the aperture shape, each positioned according to where its source sits relative to the aperture. The O-shaped source, being extended, projects many overlapping copies of the "F" arranged in an "O" pattern.
Extended source, small aperture (e.g. "7"-shaped bulb, crescent-shaped hole):
This is the key conceptual twist. Each point on the extended source projects an image of the aperture shape (not the source shape) onto the screen.
The result on the screen is many overlapping crescent shapes, arranged in the inverted shape of the source. So you see a pattern of crescents forming an inverted "7".
The critical insight: with a small aperture, the screen image resembles the source shape made up of many copies of the aperture shape, all inverted.
The pinhole camera principle is how camera obscuras work, and it is the basis of pinhole photography. Solar eclipse viewers use the same idea: a small hole projects an image of the sun onto a surface. Extended-source imaging through small apertures explains why, during a partial eclipse, the dappled light under a tree shows crescent shapes rather than circles.
Students often think a pinhole projects the shape of the aperture regardless of the source. That is only true for a point source. For an extended source, the screen shows the shape of the source, made up of copies of the aperture shape.
When asked which optical elements can form a real image, students sometimes include diverging lenses or convex mirrors. Neither can form a real image of a real object.
In two-lens ray tracing, students sometimes forget to invert the image orientation at each lens. Track whether each lens inverts or not, and multiply through.
For pinhole image sizing, students mistakenly apply the thin-lens equation. Pinhole imaging uses similar triangles, not 1/f = 1/d_o + 1/d_i.
The "identify the unknown optical element" question is a favourite free-response problem. Know the four possibilities (converging lens, diverging lens, concave mirror, convex mirror) and which can produce real, virtual, enlarged, or reduced images.
Pinhole and mask imaging questions appear regularly. Practice sketching the screen image for combinations of source shape and aperture shape.
Two-lens ray-tracing problems test whether you can locate images graphically without equations. Make sure you can trace the three principal rays for both converging and diverging lenses.
When a converging lens is replaced with a diverging lens of the same focal length, the image changes from real/inverted to virtual/upright (relative to the object for that lens). Students who rush this problem often get the orientation wrong.
True or False: A diverging lens can form a real image of a real object.
False.
True or False: A convex mirror always produces a virtual, upright, reduced image.
True.
Fill in the blank: In pinhole imaging, the image on the screen is ______ (upright/inverted) relative to the source.
Inverted.
True or False: When an extended "7"-shaped source shines through a small crescent-shaped hole, the screen shows a crescent shape.
False. The screen shows an inverted "7" made up of many small crescent shapes.
Fill in the blank: A converging lens produces an enlarged real image when the object is between ______ and ______.
f and 2f.
Q: An object is placed to the left of an unknown optical element, which forms a real image. Which of the following could be the unknown element: converging lens, diverging lens, concave mirror, convex mirror?
A: Converging lens (yes, if the object is beyond f) and concave mirror (yes, if the object is beyond f). A diverging lens always makes virtual images of real objects. A convex mirror always makes virtual images. So only the converging lens and concave mirror are possible.
Q: If the real image is also enlarged, can you narrow it to one element?
A: Both a converging lens and a concave mirror can produce an enlarged real image when the object is between f and 2f. You cannot narrow to a single element without additional information about which side the image forms on. The object must be between f and 2f.
Q: A small bulb shines through an "F"-shaped hole in a mask. The bulb is 40.0 cm from the mask and the screen is 50.0 cm behind the mask. The "F" in the mask is 3.50 cm tall. What is the height of the image on the screen?
A: By similar triangles, h_image / h_mask = (screen distance) / (source distance) = 50.0 / 40.0 = 1.25. So h_image = 1.25 x 3.50 = 4.375 cm. The image is an inverted "F" that is 4.375 cm tall.
Q: A "7"-shaped extended bulb shines through a small crescent-shaped hole onto a screen. Sketch what appears on the screen.
A: Each point on the "7" projects a small crescent onto the screen. The crescents overlap to form the shape of the source, inverted. The screen shows an inverted "7" composed of many small crescent shapes.
Pinhole imaging connects to the wave-optics unit through diffraction: if the pinhole is too small, diffraction blurs the image. Ray tracing through lens systems is the foundation for understanding optical instruments (microscopes, telescopes) and multi-element camera lens design. The "which element can produce this image" reasoning applies to every mirror and lens problem in the course.
Pinhole camera, camera obscura, ray tracing, principal rays, converging lens, diverging lens, concave mirror, convex mirror, real image, virtual image, virtual object, two-lens system, extended source, aperture imaging, mask imaging, inverted image, upright image, enlarged image, reduced image, ray diagram, similar triangles, image formation