Calculate the height of the image formed by a pinhole camera of length 12cm used to photograph an object 60cm away from the hole and 70cm high

Analyze the question

A pinhole camera forms an inverted image on the screen at the back of the box. The length of the camera (12 cm) is the image distance (hole to screen). The object is 60 cm from the hole and 70 cm high. We need the image height.

Concept

Light travels in straight lines through the pinhole, so the object and image form similar triangles. This gives:

Magnification = image height / object height = image distance / object distance

Solution

• Object height, h₀ = 70 cm
• Object distance, u = 60 cm
• Image distance, v = 12 cm (camera length)

hᵢ / h₀ = v / u

hᵢ / 70 = 12 / 60

hᵢ = 70 × (12 / 60)

hᵢ = 70 × 0.2

hᵢ = 14 cm

Answer

The image height is 14 cm, which is option D.

Tip

For pinhole camera questions, write down the ratio (image height / object height = image distance / object distance) straight away. Always match "image with image" and "object with object" on each side of the equation. Quick check: 12/60 = 1/5, and 70 ÷ 5 = 14.