Experiment 15: Shadows, Reflection, and the Pinhole Camera

Light travels in straight lines, and three classic instruments prove it: the shadow, the mirror and the pinhole camera. This experiment builds the pinhole camera, works the mirror's reflection law, and then meets the simulation's thin lens — three devices, one rule, and image geometry you can predict with ratios and the lens equation 1/f = 1/dₒ + 1/dᵢ.

The physics behind the practical

Because light travels straight, every point of an object sends a ray through the pinhole to exactly one point on the screen — and rays from the top of the object cross to the bottom of the screen. The image is therefore inverted, and its size follows similar triangles: magnification = image distance ÷ object distance = screen distance ÷ object distance for a pinhole. Slide the screen back and the image grows — dimmer, too, since the same light spreads over a bigger area. A smaller hole sharpens the image (each object point maps to a smaller spot) but dims it further: the classic sharpness–brightness trade-off.

Mirrors obey the law of reflection: angle of incidence = angle of reflection, both measured from the normal (the line perpendicular to the surface). A plane mirror's image is virtual, upright, same size, and as far behind the mirror as the object is in front. Lenses bend light instead of blocking it. For a thin convex lens of focal length f, an object at distance dₒ forms an image at dᵢ given by 1/f = 1/dₒ + 1/dᵢ, with magnification m = −dᵢ/dₒ — the negative sign means inverted. Outside the focal point the image is real (projectable on a screen); inside it, the lens makes a magnified virtual image — the magnifying glass.

Variables and controls

In the virtual lab

The sim is a thin lens (focal length f = 10 cm) imaging a candle. Set Object distance to 30 cm: the readouts give Image distance 15 cm, Magnification −0.5 and Image type: Real, Inverted, Smaller. Move the object to 20 cm (two focal lengths) and image distance equals object distance, m = −1. At 15 cm the image is 30 cm away and twice size. Now slide the object to 8 cm — *inside* the focal length — and the image type flips: virtual, upright, magnified 5×, on the same side as the object; no screen can catch it. The ray diagram redraws for every setting, and the Data Visualization plots image distance against object distance. Log object distance, image distance, magnification and type for at least four settings, verifying each against 1/f = 1/dₒ + 1/dᵢ.

Hands-on: the pinhole camera and the mirror

Cut a ~1 cm square in one end of a shoebox, tape foil over it and pierce the foil with a pin; tape tracing paper over the open end as the screen. In a darkened room, face the pinhole at a bright window or an LED arrow and examine the dim, upside-down picture on the screen. Measure image height at screen distances 10, 15, 20 cm. Take care: never look at the Sun through a pinhole or lens, and let a hot lamp cool before handling it. For the mirror: lay a protractor printout under a small mirror standing on edge, shine a torch along a chosen incidence angle, and measure the reflected angle from the normal.

A worked investigation

(a) Pinhole. Arrow object 12 cm tall, 60 cm from the hole:

Step 1 — Magnification at 15 cm: m = 3.0 ÷ 12 = 0.25, and the ratio rule gives 15 ÷ 60 = 0.25 ✓. Step 2 — The constant 0.20 is h_object ÷ d_object = 12 ÷ 60: image height is simply screen distance × that constant — linear growth, predicted before the box is even opened. The image was inverted at every setting (rays cross at the hole) and noticeably dimmer at 20 cm than at 10 cm.

(b) Lens (sim, f = 10 cm).

Step 3 — Check dₒ = 15 cm: 1/dᵢ = 1/10 − 1/15 = (3 − 2)/30 = 1/30, so dᵢ = 30 cm ✓. Step 4 — The dₒ = 8 cm row's negative dᵢ is the mathematics announcing a virtual image before the sim's readout does: the lens equation never lies, it just changes dialect.

Conclusion and evaluation

Straight-line geometry predicted the pinhole images exactly (ratio constant 0.20, inverted, dimming with size), and the lens equation reproduced every sim readout including the virtual case. Pinhole measurements carry parallax on a dim image — the screen edge is fuzzy — and the foil hole is never a perfect point, which caps sharpness no matter how carefully you measure. The sim sidesteps those messes (ideal lens, exact distances), which is why the two approaches complement each other: geometry from the sim, honest image quality problems from the box.

Safety

Never view the Sun directly or through any lens or pinhole arrangement; let lamps cool before handling; take care with scissors and pins when building the box; keep the darkened room's walkways clear.

Common mistakes

• Measuring mirror angles from the surface instead of from the normal — incidence and reflection are both defined from the normal.
• Calling the pinhole image "upside down because the box flips it" — it is the crossing of straight rays at the hole; that is the explanation to give.
• Huge pinhole — a big hole passes many rays per object point: bright but blurred; judge the trade-off deliberately.
• Expecting a screen image in the magnifier case — a virtual image cannot be projected; the sim's "virtual" readout is the clue.
• Sloppy distance origins — lens distances run from the lens centre, pinhole ratios from the hole; measure from the optics, not the box end.

Exam Experience

Question 1 — calculation [4 marks]. A pinhole camera photographs a 2.0 m doorway from 8.0 m away, with the screen 0.20 m behind the hole. Calculate the image height and state its orientation. A student then doubles the screen distance; state the two changes to the image.

Scoring guide:

• Magnification = 0.20 ÷ 8.0 = 0.025 [1]
• Image height = 2.0 × 0.025 = 0.050 m (5.0 cm) [1]
• Inverted [1]
• Doubling screen distance doubles image height and makes it dimmer (same light over four times the area) [1]

Question 2 — evaluation and design [4 marks]. Design an experiment to investigate the trade-off between pinhole size, image brightness and image sharpness.

Scoring guide:

• Independent variable: pinhole diameter (e.g. 0.5, 1, 2, 4 mm in interchangeable foil cards); all distances fixed [1]
• Dependent variables: brightness (light-sensor reading or standardised exposure judgement) and sharpness (smallest resolvable gap/letter on the object) [1]
• Controls: same object, lighting, screen distance and darkening across hole sizes [1]
• Repeat each size and present brightness vs sharpness together so the trade-off (bigger hole: brighter, blurrier) is demonstrated quantitatively [1]

Multiple choice 1. The pinhole image is inverted because:

• A. The screen bends the light
• B. Light travels straight, so rays from the top of the object pass through the hole to the bottom of the screen
• C. The box acts as a mirror
• D. Gravity pulls the light downwards

Answer: B. Straight-line propagation with a single crossing point — the hole — swaps top and bottom (and left and right).

Multiple choice 2. A torch beam hits a mirror at 35° from the normal. It reflects at:

• A. 35° from the surface
• B. 55° from the normal
• C. 35° from the normal
• D. 90° from the normal

Answer: C. The law of reflection measures both angles from the normal and makes them equal.

Going deeper: the family of image-makers

The pinhole camera has famous descendants. Renaissance artists used the camera obscura — a room-sized pinhole — to trace projected scenes; photography began when the screen became light-sensitive film; your phone camera is a lens system solving the pinhole's brightness problem by gathering light over a wide aperture and focusing it, trading the pinhole's infinite sharpness-everywhere for light hunger and shallow focus. The mirror, meanwhile, works double duty in a periscope: two mirrors (or prisms) at 45° pass an image over an obstacle, each obeying θi = θr, the pair restoring the orientation the single mirror reversed.

Keep the sign language straight across all of them with the summary your worked data earned: pinhole — always real, inverted, size set by distance ratio; plane mirror — virtual, upright, same size, as far behind as the object is in front; convex lens — real and inverted outside f, virtual and magnified inside f. Three devices, three personalities, one ancestor principle: light travels straight until an interface gives it new instructions.

One more angle: pinholes in the wild

Nature builds pinhole cameras for free: the gaps between overlapping leaves act as pinholes, and on a sunny day the "coins" of light dappling the ground under a tree are not leaf-shaped — they are *images of the Sun*, each round because the Sun is round. During a partial solar eclipse those dappled discs all turn into crescents simultaneously, the safest solar observatory there is: you watch the ground, never the sky. It is the shoebox experiment running at forest scale, and noticing it is a fair test of whether the straight-line model has really landed — the world keeps projecting images; optics is learning to read them.